I put the prints in the developer face down and gently push them under with my gloved fingers. I use tongs for test strips and prints I know won't be final. Much less likely to damage prints by hands. I use nitrile gloves and wash them after each print, like I was washing my hands. Then dry them before taking them off. That last for many printing sessions, so there's little cost.
Some developers keep better than others. I've been reusing and replenishing the same batch of Ansco 130 for over a year now. It still develops quickly with excellent DMax. I use water for a stop bath and a neutral fixer. All of this is odorless and causes no discomfort in the darkroom. I don't usually run the fan with this chemistry. I would if I was using an acetic acid stop bath, or an acid based fixer. I'm sure someone will say I should use the fan anyway, but I'm not convinced.
I wouldn't run a table type fan while printing. It's a sure way to add more dust to the paper than it looks like you already have. It also helps to keep the cats and dogs out of the room and vacuum frequently (ideally with the exhaust of the vacuum outside the darkroom).