gap between wall and ceiling before mudding?

Hello Forum, Our house was built in 75, brick with studs. Only one layer of brick i think. So starting from the outside is a layer of brick a space of about 3" then OLD cement board stapled to the studs, insulation and drywall. My drywall started to mold in the closet about a foot above the baseboard. I cut the wall apart took out the insulation and the paper on the OLD cement board was moldy. Some how water is getting in but once i figure out how its getting in what do I need to do? I live in central Texas. I'm worried that a lot of the cement board is moldy. Can I put plastic in between the stud cavity's tape it then re-insulate?

Long story short, I have a small 2x4 AC plywood that was skim coated, primed and then painted... It's been around 8 years and now it's started to just crack and the paint/skimcoat JC is peeling right off the AC plywood. I plan to just scrape it down to bare wood and refinish again... Does plywood in general need to be primered before skim coated. I am planning to use Zinnsers primer before skim coating this time around