Welcome to wine making talk. Wine is fairly forgiving so you will hear several different methods. Listen for the why and then make a choice.
*mold is a risk on anything that floats, whether fruit or plastic balls to fill the headspace in a carboy, therefore punch down till all floating material is removed.
*I aim for 1.020 to 1.010 for pressing fruit pulp and putting a country wine under air lock. From a yeast point of view they have reproduced all they will at 1.040 so they have no additional need for oxygen. Some white grape recipes do the whole primary under air lock. At 1.020 the yeast is actively producing CO2 so it will recover an anaerobic environment. You might get more flavor if you let the wine on the pulp in till 1.000.
*you didn’t mention if your cherry is pitted. So far I have not pitted cherry. I am seeing off flavors develop at 18 months, next time I do a cherry I am going to pit a couple of gallons and see if off notes don’t develop. (cherry pits have cyanid in them/ my current choke cherry started with astringent notes therefore I wonder if long chain tannins are in all cherry species), ,, anyway pits are another argument to remove pulp sooner rather than later.