1) Sounds like you're visiting a site with Flash. Safari + Flash = 100% CPU usage = hot CPU
3) That's what happens when you put a lot of cycles on the battery, especially when you drain to 0% and charging to 100%. Download coconut battery to see how many cycles you've accumulated; I'd guess about 150. Apple says their batteries are good for about 300 cycles, but you'll see quite a bit of degradation in battery life by the time you hit the 300 cycle mark.