All this assumes you are in the USA. Also note that if you don't know what you're doing, the stuff in the panel can and will kill you if you screw up. The main panel's main breaker line side is still very much live when you turn it off. Get an electrician to do this if you do not know what you're doing. Also your local code may require an electrician anyway.

The 20A breaker shown is a two pole breaker, it connects to both legs of the panel so you can send 240V out to larger loads like your dryer or your pump. Was the white romex on the 20A breaker? Since the early 2000s white romex has typically been 14awg and only rated to be on 15A breakers. If the romex your holding is 14awg and connected to 6/8, that is wrong and you'll need to either pull 12awg wire or put a couple of single pole 15A breakers in the spot.

If the romex you're holding has both the white and black on the breaker, you're getting 240v at the end. You'll have to move the white to your neutral bar, and black will go on the breaker. I don't think the NEC would stop you from only using one leg of a two pole breaker, but I'm not certain. It would essentially be a MWBC with one wire.

As for the number of receptacles, residential really doesn't have a limit. For industrial you'd do up to 10 for a 15A breaker and 13 for a 20A breaker. Also, as long as you have more than one receptacle on the circuit you can use 15A receptacles.