How can I remove peeling paint from drywall without damaging the drywall or texture? Is there a chemical stripper that you can recommend?
Using a paint stripper on drywall is not an ideal approach, and requires special care: water-containing strippers can soften and ruin the paper and texture. Solvent types can also sometimes cause problems, so it would be wise to do some test areas before proceeding.
Try a gel-type solvent-based paint and varnish remover. It is essential to use ample ventilation, with windows open. Small areas should be done at a time, with all trim, doors, floor, etc. protected with heavy cotton dropcloths. Apply the remover with an inexpensive "chip brush", and leave it in place only long enough to soften the paint. Remove the softened paint carefully using a 3" blade putty knife, drawing it backwards. Hold a double-bagged paper bag underneath to received the removed paint. Again, do a test area to assess impact on the paint and the drywall.
Before moving ahead with the stripping, remove as much of the peeling paint as you can by simply pulling it off, folding each piece back on its self and pull back away from the edge of attachment. Keep all children and pets away from the area. Wear eye and skin protection, and preferably wear a respirator that is rated for chemical fumes.
Once stripped and dried, go over the area with a damp sponge and rub off all residual paint. Once thoroughly dry, apply a latex stain-blocking primer. Wallpaper or latex paint can be applied to that.