Ok, first of all, the back brakes. The back brakes have an adjustment at the back where the cable hooks to the lever on the brake housing. It should be a wing nut type thing on the end of the cable. There are two cables, one is for the brake pedal and the other is for the left front hand brake/lever. There's a place for a small wrench to hold the cable while you turn the wing nut type thing. If you don't hold this nut, the cable will twist and probably break and then you will have to replace the cable. While in neutral, adjust the cable up a little at a time, while pushing the 4-wheeler back and forth a little to make sure you don't get the brakes too tight. If you feel it start trying to hold the 4-wheeler when you are pushing it, back the adjuster back off just a bit, until it rolls free. On the other hand, I'll bet your brakes are wore out to the point where they can't be adjusted anymore. Brakes on these models usually don't last long if you ride through much mud and water. The brakes are sealed, but the gaskets usually end up letting mud and water through, anyway, and then it is trapped in there. There is a drain plug in the bottom of the brake housing that you can loosen occasionally to let water and mud run out. It is hard to see for the skid plate on the bottom of the housing. When you do replace the rear brakes with new ones, the new ones will stop you, but they won't be great. You will have to push the brake pedal pretty hard. There isn't much you can do about it. They were like this when they were new.
The front brakes may need to be adjusted up and bled.
If you are talking about the front reverse lever/parking brake handle(this lever works both the back brakes and the reverse. You have to push the red button down to engage the reverse cable.), there is an adjustment at the same place as you adjust the back brakes. There are two cables back there. On is for the back brakes(foot brake pedal), the other is for the hand brake lever(parking brake). When you adjust this cable, it will tighten the left hand lever back up. I think this is what you are talking about as they all do this and even after you adjust it tight, in a few days it will be back like this again. I just got used to it.
As far as the lights getting water in them, make sure the rubber boots that go over where the socket goes in the lens, are in place and tight. They will only go on right one way, there is a notch it has to fit in. The notch is at the top. This is may be hard to understand, unless you are looking at the boot and the back of the lens where the bulb goes in. If this is not your problem, your lens might be cracked somewhere. If it is, dry the water out some way and put some silicone over the crack.
The lever at the top of the head is a decompression lever. Pushing this lever down, while tying to start with the kicker, will make it kick over a little easier. I don't really think they even needed to put one of these on a 300, as they kick over easy, anyway. There is a seal where the decompression lever shaft comes through the head. This could be leaking or it could be the round black rubber plug beside it, between the valve cover and the head. Both of these items tend to start leaking after they get a little age on them. I wouldn't worry about it too much, unless they are leaking bad. Most of the time, they just leak enough to get your engine a little oily. If you don't like oil on you engine, then you will have to replace one or both, depending on which is leaking. If you don't replace them, just keep an eye on your oil level.
If you are new to repairing ATVs, it would probably be a good ideal to get a repair manual.