Sterilizing

you can use purified but not distilled. you can also just use tap water thats what we use.

Updated

you can't use distilled water to make formula but you can use purified...u can also use tap water. thats what we always use

I do. The water is purified so why not?! It's cheaper!

It would depend on the type of pipes you have in your house. Older homes may have lead in the pipes. I would also check out the city water evaluations. Those documents are public.
As mentioned below, flouride is not so good. I refrained from tap water, for the first year, due to flouride being added to the water in my area.

It depends on whether or not your water source has floride. If you don't have floride in your water (i.e., you have a well) then you should use bottled water that does have floride (or give floride supplements - which can be expensive).

no distilled, but if it's just filtered in your fridge, that's fine.

Absolutely. That's what we did with my son, and his pedi was fine with it.