Need Pro Advice On Ceiling Drywall

You can either tear the 3/8" off and see what's under it, (and repair it) or add 1/4 or 3/8" or 1/2" to the entire ceiling that needs it. It's a good idea to glue the drywall between joists when overlaying a ceiling. I'd probably tackle whichever room is smaller.

Good job!

Hard to say without a picture. Are you sure it is drywall or could it be plaster? Drywall will usually have 4 ft long seams. Gypsum lath was used with plaster veneer prior to drywall. (1950s) It looks like drywall but the pieces are smaller.

Sometimes surfaces that were painted with latex over oil based paint will peel because the oil based paint is so slick it doesn't bond. Or it could indicate a moisture problem. Or it could be veneer plaster peeling off. Depends on what you have... the age of the house might help.

Yep, that's typical for a post wwII house. Anything that is peeling, yes you need to scrape it off. Use a stiff putty knife and chip away at it until it no longer chips off.

If you are concerned about lead paint in your home during your rennovation, see this site.

I would probably prime the slick oil based paint with an oil based primer like Kilz original. It will leave a flat finish that your joint compound will stick better to. You could also use Gardz, but it is kind of a pain to work with because it's so runny.

Then you can prime over your drywall repairs again with most any kind of primer before you paint. You do that so that the sheen of your topcoat isnt affected.