No filter is fine ,you just need to do regular water changes, but i would suggest you have a heater unless you have a very warm room thet stays that way all year round - even so a heater would probably be better
Nope, you don't need a filter, I've never used one & never had any problems.
Just make sure you clean the water weekly, & heaters aren't necessary unless it is cold where the location of the tank/bowl is, or if you can't get the water to stay warm enough.