You can make an "exception" for that via, so it is covered with solder resist. It's called via resist "tenting"- but the resist might "slump" if the hole is large.
No you don't have to, but you can if you prefer. Easiest way for a straight forward pcb design is Settings=>Design Tech=>Layer Types. From row names Solder Mask you can toggle various types of pads & vias ON/OFF etc.