Taking things in reverse order:
With the large areas firstly remove any remaining loose plaster. Trying to patch without doing this is a waste of time. Then with the large areas you'll need to replaster. You can either take this as an opportunity to learn or pay someone. I won't tell you how to plaster as it's really a skill you have to be shown or practise yourself, though I do have a couple of bits of advice. Don't try to plaster the whole wall in one go. Take it in stages and make sure you dampen the wall you're plastering onto as it helps the plaster stick.
With the areas missing the top coat of plaster you will need to reskim. This should be done after fixing the base coat. You might find a plasterer willing to skim over your base coat - discuss it before you start. This will give you a good finish but should cost less than hiring a plasterer to do the whole job. Getting a good skim finish takes a lot of practice.
Finally the areas with only minor cracks and bumps should be filled and sanded before proceeding.
If you manage to get a good surface then painting is the best option. If not then paper the wall with two layers of lining paper. The first runs horizontal and the second vertical. This will smooth out most of the remaining unevenness in the wall. Before papering wash the walls with a weak glue solution this will stop all the glue from the paper being absorbed into the plaster and the paper lifting off the wall.
I should have added that you need to leave the plaster to fully dry out before painting or papering. That might have been one of the reasons why the previous repair has failed.
UPDATE
The quote you have doesn't seem unreasonable but without knowing the exact area you need replastering or your location it's difficult to say for certain. However, we shouldn't be getting into commenting on exact quotes as they are always going to be too localised (in time and space). Get another quote to compare it against - that's always going to be the best option. Also as I said above see if you can get the plasterer just to do the final skim - it should come out cheaper.
You do need to seal the plaster otherwise the new paint won't stick as you point out.
My first choice would be to wipe down and then paint with a coat of diluted emulsion as you suggest. You might want to try this on a section of the wall before doing the whole lot to see if you get a good finish.
Dilute PVA will definitely seal the plaster and I can't think of an obvious reason why you shouldn't use the wood glue - but there may be differences in the formulation you need to look out for. How dilute did you make the mixture in the past? I've used a 5:1 water to glue ratio for sealing a ceiling I was going to paper which worked well. Again you could try a higher ratio to see if you can find a mixture that still seals but then accepts paint better.
You might be better off sealing with the dilute PVA then putting up lining paper - which does stick quite well - and then painting that. The benefit here is that the lining paper will smooth out the wall further hiding any remaining imperfections.
Of course the solution that will give you the best finish is to get another skim coat of plaster applied.
Best Answer
Firm plaster should be reattached with plaster washers and drywall screws. Fix damage areas with patching for use on plaster and apply an oil-based or shellac primer to seal out moisture. Follow with a top-quality latex paint to give your old plaster a new look.