I have bumpy plaster also. I use fiberglass tape on cracks. There is a new, thinner variety out there that you can get at home depot and I would recommend that. I create a texture with my final coat of drywall compound using a sponge and this funky faux painting tool I picked up years ago (it has tons of little rubber fingers on it) but if texturing primer works for you go for it. I'm guessing that your texture came from a sand paint originally anyway. Use thin layers (at least 3). You'll get better as you go an there will be less sanding as your technique improves.

I have never run into chalky plaster so I'm no help there. The bulges you describe could be because the keys in the plaster that attach it to the lath have broken. You might want to research plaster washers or broken plaster keys and see if that is your problem.

I don't use oil primer but I do prime my patch once, then prime the whole surface and then paint one or two coats of color. The repair will absorb paint differently than the old painted plaster and the paint layers will help the repair blend in. I'm glad you are taking the time to repair your walls. It will be worth it. And someday if you move to a non rental place that needs repair you will have the learning curve behind you.

Oil based primer helps hold the surface together without adding additional water.

There are some latex paints that claim to perform the job, but since they contain water it is going to soak into the plaster.

Large soft areas that show fine cracks may need to be removed down to a solid layer and repaired.

Easysand is a setting type drywall compound available in a range of setting times that works well (and can be sanded if required).

Durabond is so hard it really cannot be effectively sanded, but is as hard as old plaster.

Either compound should be mixed as thick as smooth peanut butter for patching plaster.

It WILL take longer than the time on the bag to fully harden, but you can apply another coat once the first has hardened even though it may not appear dry.

These compounds harden by chemical reaction, not by drying out (like pre-mixed drywall compound).

The hardening is not reversible or alterable by adding more water.

More water just makes the compound shrink as it hardens and not be as strong.

You can also buy adhesive fiberglass mesh in 3 foot width. It's a two person job to put it on neatly and more than a little tedious to cut around window moldings, baseboards and other things, but it will strengthen old plaster walls like nothing else. The first coat of compound should just fill the openings in the mesh. Subsequent coats and sanding smooth it out.