With my 10 gallon community tank, I take out 25% every week and replace it with fresh (dechlorinated) water. I do it because the filter needs the beneficial bacteria. With anything smaller than a 10 gallon, it's hard to get a steady cycle so I don't bother.

Since there's no use cycling your 3 gallon, I'd do a 100% change every week/week and a half. I wouldn't use bleach though.. it wouldn't take much residue to kill a betta. I'd probably take out the filter too. No use cycling and most bettas don't like the current.

As for the food, you can either syphon out the left over pellets, or fast him for a day or two. I do it (unintentionally LOL. I get busy with work) and they've never, ever refused food after a day or two. It's no biggie if you leave it though.. since weekly WCs on a 3 gallon will leave your betta with clean water constantly.

2.) Feesh has really long fins. They change from blue to red in different areas. Recently, within the last couple of days, his fins have started to curl at the ends as a flower petal would, and darkening. This is at the very ends. They are also become slightly stringy, also at the ends.
Sounds like fin rot. Not hard to treat fortunately. Just keep up with water changes and add a bit of aquarium salt when you do WCs. You can also add a bit of melafix/bettafix if you'd like. I've never noticed a difference when I've used it though.