As already mentioned in the comments the biggest problem will be food. But is it really? Not for a year (if he doesn't mind some possible malnutrition).
Luckily he arrived just after THE EVENT, so a lot of resources are available
Resources
But let's see what resources are actually available to him (assuming he arrives in/near a big city):
- His Universe Traveling Power (which is mind-based and doesn't help him).
- Vehicles. Some will be crashed due to being operated at THE EVENT, but there'll be a lot of vehicles still working and fueled.
- Clean water. Almost all facilities are still operational, and water won't go stale. He can simply collect all water supplies he can find before the facilities stop working. He has to hurry though, as this might happen quite fast.
- Housing. As DJMethaneMan mentioned he has all the housing in the world, and most buildings should easily survive one year without maintenance.
- Food. He actually has plenty food available to him. As mentioned by SF no food will rot... initially. The greatest threat for his food supply is actually himself. He carries the bacterias that can destruct his food inside himself. While those might usually not be the most effective destructors, they have absolutely no concurrence and can develop freely. Packaged food will be his best bet.
Let's ramp up the difficulty a bit:
Assume he arrives far from bigger settlements, like near a small settlement (maximum 50 inhabitants).
- Vehicles. Still likely to find some. They will probably be more durable, but also older (fuel might become a problem). If he wants to use them he'll have to fetch it from the next big town (most likely).
- Clean water. It is pretty likely that a lot of the houses will have their own wells or a small river nearby. When he checks the water quality regularly (some chemicals might enter the water at some later point) and keeps a reserve (remember, water won't go stale), he should be fine.
- Housing. Durable houses, likely standing for many years and still standing in a few years. No problem here.
- Food. As such settlements can easily become disconnected from major cities during winter, there'll likely be some food stored in every house. It should definitely be enough for one person to survive a year. He is still his own greatest enemy.
Going extreme now. He arrives in a total wasteland, the next settlement is 500 km away. Normally his friend would've picked him up, but he overslept, now the friend is still in the bed and the car is in the garage 500 km away.
- Vehicles. Not existent. He has to walk.
- Clean water. Possible, if any natural water is nearby. But that is basically luck-based.
- Housing. If he is lucky he will find a cave to hide from the weather, but the perfect cave is extremely rare. If he wants to stay at a place he should build his own shelter with some of the dead wood and leaves. If that is not present he is pretty screwed.
- Food. Not available for a year. If he is lucky he finds some animals which he can eat, but this will not last a full year. If he is lucky, healthy and trained he might be able to make it to the next settlement. The biggest problem is not that there aren't animals, but to find these animals with an appropriate effort. A lot of animals will most likely be hidden somewhere, and out traveler will spend a lot of energy to find them.
Dangers
Note: I'm no expert in this area. I had some biology and geography classes and I derive the following chapter from this knowledge
- Fire At first nothing will actually happen. The wood is still as wet or dry as it was just before THE EVENT, so the danger of fire is not higher than usual. During the summer months the wood, grass etc will become dry though, and the danger of brushfires will increase in areas where that was no topic before. The best bet for our traveler would be a natural wet area, despite the other problems that come with such an area. Luckily he will not catch an illness or be hunted by predators, as they are all dead.
- Storms are only of the usual problem. He will not be warned beforehand, so he should try to immediately move outside of typical hurricane, typhoon, or similar areas. Despite from that a solid house should suit him easily for a full year. He should store his resources accordingly so the won't get blown away.
- Low temperatures While of course a problem in itself, it shouldn't bother him very much with a little preparation. There is plenty of usable wood in the countryside, many tools to prepare it in the houses (though he might have to search a bit) and if everything fails there is the furniture, which is more often than not made of wood (he only needs one set for himself).
- Floods Usually easily avoidable by moving higher. Most big cities have houses with rooms that are always above the water-level, or some hill nearby. Huge plains might provide a problem here, but he can build walls beforehand. Lots of manhours required here.
- Diseases What? After all the times where I said they won't be a problem? Yes. He can not catch a cold from others (though he should stay away from humans in the first weeks because of viruses), he still carries a lot of diseases inside him. He is adapted to most, but if his immunity-system is slightly impaired (due to being caught in the rain without protection for example) these diseases might break out again. That a disease evolves inside him and harms him is so unlikely that he can't do much against it. And most medicine will survive one year until he can get professional treatment.
- Nuclear Fallout The silent killer, radiation is surely a threat. Luckily reactors won't blow up in the second they are unsupervised, if at all. Most will turn themselves off. Those that actually leak radiation... the simplest solution is to move away as soon as you realize there is a nuclear power plant nearby, before anything could possible happen inside the reactor. As they are usually easy to spot, this shouldn't be the biggest problem.
- Power Shortage This is highly based on chance, but the power grid will fail extremely fast without maintenance. The problem is not based in the generators. While any fuel-based generator will soon run out, there are many portable generators available (just look around a bit) and fuel is also available for free. Also the renewable generators will supply the Power Grid for quite long before failing, and most users of electricity are now off-line (and dead. Mostly dead).
The problem is the grid itself. The huge cable-network needs to be constantly repaired. While it may easily survive the first weeks, It will break more and more, eventually disconnecting the traveler from the Power Plants. This is where the mobile generators come into play again.
- Mental Breakdown This is an actual danger. He just entered the ultimate apocalypse. Everyone is dead, and even worse will stay in the same state for the rest of the year! If the destructors would be still active the corpses would eventually become skeletons which are much easier to handle by the human mind (but are still troubling). But his loved ones will stay in the state they were in at the moment of their death when they are outside the wind/rain/etc. might change their appearance, but that would probably even worse than those inside.
To make it even worse, every human he touches will be infested with the destructors he carry inside him. As the first humans he will voluntarily encounter are most likely friends and family, he would be responsible that their bodies will be destructed while every other body stays in the same state. While this is of course unimportant for the dead, it might severely harm his state of mind. After all now his loved ones look like corpses, while everyone else looks more like asleep. He is literally the most destructive living being in the whole universe.
Luckily he has a lot of stuff to spend time on. There is a lot of work that needs to be done, and he has electricity to watch films, use a computer (for games), hear music ect. He will need psychological help afterwards, but he can survive it.
Conclusion
It will be hard, but definitely possible. If he wants/has to stay longer he has to prepare much better. He will be a scavenger forever. If he is an exceptional scientist, he might be able to transfer some of his vis vitalis into some gene samples (maybe he finds a way to manipulate the very essence of life to adapt it to almost similar genes, going further and further from there), but this at best unlikely and at worst impossible. Best thing I can assure that if he is ready to move every few years he should be able to live his full lifespan without ever being in great need.
The greatest threats are injuries and sudden events such as earthquakes, brushfires (he will have to plan accordingly) or 16 km-diameter-meteor impacts (anything smaller is also dangerous).
What comes next?
This is highly speculative and more a bonus section. The fact that there is no life makes this hard to predict
Unimportant whether he is still there or not, the world spins further. Nothing will rot, but stuff will still become unusable.
In 10-20 years, all trans-regional power-lines will be broken.
Storages for dangerous materials will show first weaknesses which would usually have been detected by humans early on.
Almost all but the most static building will show at least some structural weakness.
By now, fires will have burned down most major cities, though there'll still be much to scavenge in these towns.
Almost all vehicles on tires need their tires to be changed, as the material weakens and the air will escape. Spare tires may still be operational, but will break soon after.
Electrical devices will become nonfunctional due to water and dust getting inside. If properly stored they can of course last much longer.
Most food will still be good, but some chemical reactions could possibly create dangerous poisons. Eat with caution.
Clothes will remain functional if properly stored. Anything that usually eats it is dead.
After 100-200 years most building will be destroyed. Vehicles are unusable.
Any complex device will most likely malfunction in some way if turned on.
The ISS might have entered the Atmosphere and crashed, leaving a nice hole.
Wind and Water start to erode all areas as the (dead) grass and other plants are no longer able to hold it. While the erosion of course happens always, I expect this time is needed to erode earth that is still completely hold by roots.
Plants will lose their green color as Chlorophyll and other stuff breaks under the constant sun. This also happens normally, but is normally easily replaced by the plant.
Food will start to spoil the same way. Due to temperature changes stuff like Vitamin C is likely destroyed in most food. I don't know about other proteins, acids, fats etc, but I'm pretty sure they will also start to break apart as well.
What will happen in the years after that? I can only do an educated guess from here, and I'm happy with every correction.
Roads will stay for very long, but might be covered with dust. They are so flat that the wind doesn't affect them that much. Freezing water can still break them, but usually plants grow in these breaks enlarging them. Not possible here.
Towns will be visible for a long time, albeit destroyed. If at any future time an trans-universe-archaeologist will visit the earth he likely will find the former places of the major cities very easily.
Speculative: The earth might warm up a bit. As fires burn, they put huge amounts of dust in the air. The dust from eroding also will block some of the heat being reflected back to space, keeping it in the system. As no new Oxygen is created (from plants), the atmospheric composition might slowly change. While I can not foresee the results of this, it might induce a greenhouse effect.
Ultra-Extremely Speculative Thing. Not even an educated, but a wild guess: The earth might actually cool down a bit. As the surface loses its color and is covered in dust its surface albedo changes, possibly becoming brighter. This causes more of the heat reflected back to space, which again cools down earth.
