#1 - You must be in multiplayer/deathmatch mode. Can do this by setting "deathmatch 1" ( or 2, 3, 4, see
https://quakewiki.org/wiki/deathmatch ) and then loading your map. If you start multiplayer game through the menu, that's what the game basically does, setting deathmatch no non-zero (or coop 1 for cooperative play).
#2 - Maps showing in the level select menu I think are configured in a special file you can find in \Steam\steamapps\common\Quake\rerelease\id1\pak0.pak\mapdb.json though I don't know if editing it is a good idea. In case you want to experiment, don't put the edited mapdb.json back into pak0.pak (although you can always verify installation in Steam and redownload 'wrong' files), but rather pack it into pak2.pak file