Hey there Red, glad you found us here ^_^
1) No, keep it in the 10 gallon if you are able to. It's not true that smaller fish need or can be in smaller tanks. Babies are sensitive as you may have read, so having a larger, more stable tank (like a 10 gallon) will be much more healthy for your baby than to have it in a smaller tank.5.5 gallons would be okay too, but if you have the option, a 10 gallon is much better to use!
2) Never do a 100% on a baby betta or on a cycled tank. (Do you know about the Nitrogen Cycle? If not, look it up here! Or ask) A 25-50% would be adequate every other day if you keep live plants in the tank. Take care though when you add new water that it matches the old water best you can. No need to remove the baby during water changes.
3) Depends on where you look. I honestly would use a 50 Watt Hydor Theo
heater from that link. And if you want other fish later on, use an AquaClear 20
either from the store or on that link. If you don't want other fish, then you can use a simple sponge filter and air pump which will create less flow for your baby to be pushed around in but still have good filtration: Sponge Filters
and a Fairly Quiet Air Pump