Personally, I'm not sure that drones would really be the ideal way to do battle in the hypothesized scenario. The problem with your hovercraft idea is that the hovercraft itself is fairly useless unless you're trying to annoy them to death. You could put some small guns on the hovercraft then shoot at people, but you're not going to do much once they realize you're shooting at them. They'll just wait inside until you run out of fuel. You could use the hovercraft to plant explosives, but it's going to be tricky to get the explosives somewhere useful.
It would probably be much easier to design a self-guiding missile with a fairly large explosive payload and just destroy critical sections of the enemy compound than to design and pilot drone aircraft in some kind of dogfight. A missile is a sort of drone aircraft so it could apply here. One big advantage of a missile is they move extremely quickly and would be almost impossible to defend against. Additionally, the high speeds of a missile mean you can use its kinetic energy to help penetrate enemy walls to detonate inside rather than out. http://hypertextbook.com/facts/1999/SeanManning.shtml cites missile speeds of 860 m/s and higher, but a crude missile made in a few days by some random nerds would likely have a lower velocity. Still, the low air density and gravity on Mars mean you can get very good results with lower power. Depending on resources available, it could be feasible to create multiple missiles and target every building in the enemy facility at once.
With fewer missiles (or the prospect of a long development/fabrication time per missile), you'd want to be strategic about your initial targets. The specifics would depend on the actual configuration and logistics of the enemy base, but in general the priority is preventing them from counter-attacking. Unless you have access to extremely high-yield explosives, you're not likely to kill all of them quickly. So you'd want to destroy things like their life support and let them freeze to death or suffocate rather than attacking them directly.
The scientists would have access to rocket fuel (they have to leave Mars somehow) and all kinds of chemicals that that could be used to make decent explosions. Depending on the nature of the mission, they might have premade explosives for blowing holes in the local rocks. For example, mining operations. At this point, they just need to make a missile.
As pointed out in other answers, air pressure and density are much lower on Mars than Earth, so missiles would need much larger fins for guidance, at which point they would begin to resemble airplanes rather than traditional missiles. Something like the Sky-Sailor might be a good start for this, but unless you really want to save fuel, you don't need aerodynamic lift. Given the abundance of rocket scientists, you could also forego guidance fins and use maneuvering thrusters like a spaceship.
Cameras in the missile could be used to identify and aim for a target structure, making it virtually impossible to jam the device. Alternately, it could be remotely guided, or use some type of local GPS to detonate at a target coordinate, but those methods would be easier to jam and/or hijack the missile. Still, the war likely wouldn't last long enough for either side to develop methods for hacking the opponents' missiles, so it might be fine.
One problem you'd have with explosives on Mars is the lower air density. Explosions typically work by temporarily increasing the local air pressure to extreme levels which causes damage. But a thousand-fold increase in Martian air pressure is much less of an issue than a similar increase on Earth. (This is also why explosions in the water can be much more devastating than those in air.) Unless you were able to land on the surface of a structure then detonate, concussive forces will be fairly non-lethal.
However, you can still use explosives to good effect by encasing them in something hard and dense. The explosion then rips the casing apart and showers the area with high-energy fragments which work regardless of atmospheric pressure. This is the basic premise of a fragmentation grenade.
A similar idea is the premise behind firearms and some types of mines: Put the explosive at one end of a tube, then pack ball bearings or similar in front of the explosive. Detonate right before you hit the target structure and you've got a shotgun blast. There are three advantages of this method over the previous method: First, you aren't wasting much energy tearing the casing apart. Second, you can focus the energy into a small angular area which in turn means A) you aren't wasting energy throwing fragments into the sky or ground and B) you'll do much more damage to the smaller area and be more likely to tear all the way through. Third, the force of the impact isn't going to be nearly as affected by the distance to the target (a spherical explosion means the fragments per square meter decrease inversely with the square of distance, while a shotgun blast is fairly collimated and the damage decreases in an almost linear fashion).
An even better method, although trickier to pull of, is to detonate an explosive inside the enemy facility. This way the dense air inside propagates the energy much more efficiently, and damage to critical systems will be much higher. One method is an armor-piercing explosive. This type of explosive has a very dense nose cone designed to punch a hole in the wall of the facility, allowing the rest of the missile to follow and land inside, at which point it explodes in a normal fashion. A second method would be to detonate one explosive outside, creating a breach in the wall, then following right behind with the payload explosive that flies through the hole you left and detonates. A third, more Hollywood method, would be to covertly fly or drive a vehicle through the front door, down various corridors, and then explode. The best bet for pulling this off would probably be to land the explosive inside a crate outside the building and wait for the enemy to bring the crate inside for the night (or something similar). You might also land inside an open maintenance bay or airlock, then wait until it's been pressurized to detonate, but detection would be more likely.
If you don't consider missiles to be "drones" and must use something like your picture above, all of the above can be applied to a rotorcraft with explosives. However, you're less likely to penetrate the enemy structure with momentum and would almost have to use a two-stage or covert approach to get the primary explosives inside the building. A two-stage approach would be hard though, because you'd want to detonate while internal pressure is still high, and the air venting out the initial hole would blow the rotorcraft away.
Also, the size of the rotorcraft or missile is going to depend greatly on how much explosive you need to destroy the enemy compound. 5 kg might not be enough if you're trying to destroy a 100-meter dome. Here's a YouTube video of 4.5 lbs (2 kg) C4 inside a bus: https://www.youtube.com/watch?v=0nc98hzR-tk. You certainly wouldn't want to be in that bus, but the blast force goes down exponentially with distance, and even the fairly small bus isn't completely destroyed. On the other hand, domes would be extremely expensive, and likely much smaller than 100 meters.
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