There isn't a primer or sealer that will penetrate through your paint and glue it to the wall. I wish there was! Using a humidifier will help, but you need to find out where the moisture is coming from and try to stop it. Excess water vapor inside your foundation walls will eventually cause peeling and possible extensive repair later.
You are safe to patch the damaged areas and paint if the problem only manifests itself when using tape or isn't extensive. For patching the damaged areas use interior/exterior spackle or drywall compound. Apply enough to fully fill and cover the area(s), sand smooth then apply a texture to match the existing wall. Make sure to prime the repairs before painting.
A good tape that I have been using lately is Frog Tape. It does the best job with good lines. No tape can guarantee no bleed through, but Frog Tape seems to be the best on the market. Test the tape and make sure it won't cause damage. Another good tape 3M Safe Release blue painters tape. It is a 30 day tape and has low tackiness to the adhesive.