Hi. buy a very cheap damp meter. Stick it in to the wall. If the reading shows 20% or less the wall is safe to work with. Then buy a litre of shellac based stain block, zinsser bin red is the best. Open the pot, stir thoroughly and use a 4 inch medium pile mini roller with its own tray to roll the stain block on the entire affected part of the wall. As the stains are extensive, two coats would be best. Leave one hour between coats.
once complete, the application of the stain block will highlight all of the imperfections to be filled. Do not use ready mix, it’s too hard to rub down. Use a pre mix such as toupret interior filler. Flush fill the imperfections, wait to go off, then second fill the deeper imperfections as you can never fully fill them first time. Finally rub the filler down with 120 grade sandpaper. also caulk the cracks around the edges. Job done