You can do as you wish. Before they hatch they absorb the yolk. They can live off of that for over 72 hours without eating or drinking so they do not have to come out immediately. Incubator humidity and temperature don't bother them either.
It is possible that you can shrink wrap a chick by opening the incubator and losing the moisture if the egg has pipped but that does not happen often. A lot of experienced people do not worry about that.
I don't know how much, if any, harm is done by the chicks playing rugby with the unhatched eggs. No matter what you do or don't do there is some level of risk. I don't worry about them playing those games but some people do.
The way I do it is that if I have something going on in the incubator where I feel a need to open it, I open it and deal with whatever it is. If I don't see a need I leave it alone until the hatch is over.
I do agree with getting the brooder warmed up. Get it ready.