Hi everyone! First off I'd like to say I'm new here, and thanks a lot everyone for the awesome, fun, and informative site.
I'm new to betta owning (although I did have a few goldfish as a kid, and later a butterfly koi) and just brought my blue/red veil tail (still thinking of a name!) home two days ago. So please be patient with me if I ask dumb questions!

I have several, but the main one is about feeding, so...
So far my little guy seems to be doing pretty well- his colors are nice and he's pretty active. I'm keeping him in a 2.5 gallon with a 3i filter. My first question then is about water temperature. I have been researching a lot about these fish, and there is SO. MUCH. conflicting info out there!

Some say "YES get a heater!!!" and others say they're not necessary. So far I do not have one, the water has been consistently 70 degrees (read somewhere that that's on the low end of tolerable...), and my betta is active and not slow or lethargic. So if he's comfortable this way, should I get the heater? Or do you think it might be better to leave it as is?
Second question: Even running the Tetra 3i for two days the water is already somewhat cloudy... is this normal for a new tank or do I need a better filter/pump? I do know that water changes for a 2.5g should be fairly frequent (planning to do one tomorrow) but is it normal for the water to cloud that fast under these conditions?
Ok, 3rd, and most important question: having read all the panicked thread posts by new betta owners who can't get their fish to eat at first, I'm not too freaked out that mine, like theirs, doesn't eat much yet. However, there are certain things about his behavior that I don't understand. Ok, I did get him to eat a few blood worms today... but as far as regular food goes, I'm not sure what to do. He will bite a pellet, chew on it, then spit it out several times before proceeding to completely ignore it. I tried soaking pellets in garlic (which I read they like) but he won't even go up to those. Now, is this because he needs a different kind of food? I'm currently trying the standard TopFin betta pellets, which was what the pet store uses for their bettas.
Any help would be greatly appreciated!