Super speed has many weaknesses. Depending on the exact nature of the power, there are a lot of problems that could occur. If the energy for his (I'll assume male) speed comes from a chemical metabolism, then moving twice as fast generates twice as much heat in his muscles. Thinking twice as fast generates twice as much heat in his brain. Sustaining high rates of speed for long periods of time would lead to heat stroke. Even short periods of extremely high speeds would lead to death.
By far the biggest risk is probably from foreign objects though. Any uncontrolled collision, be it with a flying insect, debris kicked up from explosions, or even just bumping a door frame, would be injurious or even lethal at speeds as low as a few tens of miles per hour.
Changing direction at high speed causes very high G force loadings. The flash often runs up the side of buildings in comic books, but this would actually place thousands of pounds of force on his leg bones. If they weren't supernaturally strong they would snap.
A super speed character dodging incoming attacks first needs to be able to see the attack. This can be troublesome on its own. If he is operating at a 100x multiple (he does everything 100 times faster than a normal human) then illumination will seem either 100x dimmer, or it will be the same brightness but it will be blurry. (This straight up physics. Cameras filming slow motion video need brighter lights the more they want to slow the action.)
If your eyes can see the attack (say an incoming barrage of bullets), your brain needs to be running fast enough to process the visual data in time to do something about it. Let's say our hero's brain is running at 100x also.
In order to dodge the bullets, now his muscles have to exert enough force to move his entire body a foot or two in just a few milliseconds. That is probably going to require tens of thousands of pounds of force to be exerted, but let's say he's up to it.
Finally, that force needs to be connect with the rest of the world in order for him to move his body. This is a big problem because his feet do not have 100x more friction with the ground. (Unless he has a super friction power too?) His super strong muscles will apply tens of thousands of pounds of force to the ground within a millisecond, and the only thing that will result is that his boots will either skid across the pavement or tear apart. If he is standing next to a concrete curb though, he could brace his feet against the curb and essentially leap sideways. This might crack the concrete curb, but it would provide enough resistance to let him successfully perform the dodge.
Except now he's moving almost 100 miles per hour sideways and his feet are sticking straight out behind him. Until he hits the ground, he is helpless. He can't dodge a second burst of gun fire, nor can he alter his trajectory if he realizes his leap was poorly planned.
I think that answers questions 1 and 3. An opponent would fight him by spraying oil or slippery foam on the ground to diminish friction as much as possible. (Ideally in an unpredictable manner.) He would also want to keep launching debris into the air as much as possible in order to constrain the hero's speed. Most importantly, the hero can only react to things he perceives, so it would be critical to surprise him with attacks from concealed locations behind the hero.