With most papers, you can use a red safelight or red filter over your enlarger lens so that you can see what you're doing when you line the film up. I do that to get the framing just right, if I want clean white borders.

Yes, I always do emulsion-to-emulsion, and for bendy negs I weigh them down with a thick piece of clean glass. Everything needs to be dust free, of course.

Rather than pushing and pulling negs in and out of sleeves for successive prints, I move the neg onto fresh paper right after each exposure. Once I get things about right then I just go quickly from one print to the next.

Oh and having your enlarger at f/2.8 probably isn't such a good idea, why not stop it down quite a lot, say f/16 or more, to produce a more collimated beam. That will also improve sharpness. (And, in my experience, a contact print done through a protective sleeve shouldn't be terribly unsharp if you do have a well-collimated light source.)

Do take the time to track down any light leaks that might give you some non-collimated exposure.