I never heard of headlights rattling. From what I remember there are plastic tabs inside that hold the 2 halves of the headlight housing together, maybe yours are broken or something. Take it apart and if you can't figure it out, a little silicone or RTV will hold them together without rattling, and still be easy enough to get apart to replace the bulbs. (don't use regular glue, obviously this will make things difficult when the bulb burns out).
Your second concern, about reverse getting stuck when hot, is existent to some extent on just about every yfm350 ever built. This is caused by the clutch dragging when it gets hot. When the clutch drags there will still be a small load on the gears, enough to make it difficult or impossible to come out of reverse and usually just as difficult to find neutral when the engine is running.
The easiest and cheapest solution to this problem is that when you want to take it out of reverse or put it into neutral when the engine is running and hot enough to cause problems, get it in the gear you want to be in before you stop rolling. It won't hurt anything as long as you wait until you're stopped to continue in the opposite direction. Just try to back up in reverse with enough speed that you can throw it back into forward drive before you come to a stop, or tap it down into neutral while you're still rolling, whatever it may be that you're trying to do at that moment.
That being said, there are several ways to keep this from happening as often, it tends to get expensive though. You can add an oil cooler which keeps the temperature of the engine down, you can use higher quality oil if you're using cheap stuff now, and if your clutch is old, worn, or some cheap aftermarket brand you will likely see improvement by replacing/repairing that. Even with all of this done, you'll still probably have problems under more extreme conditions, like when you're doing a lot of slow, technical riding (most often this is when you're going to need reverse anyways) and riding on hot summer days.
