Paint liquifying around cooker: solution?
My bet is you used a water-based latex and the wallpaper has some oil in it (being over the stove there's a good chance it absorbed oil over the years). What's happening is the heat and humidity are driving the water back into the paint, and the oil in the wallpaper is interfering with the adhesion.

Two things I would do. 


Get an oil based primer (like original Kilz). It should help the adhesion of the paint to the wallpaper. Oil based should adhere, regardless of what's in the wallpaper
Put a semi-gloss enamel over it (can be water based latex). The "gloss" part of the paint will better resist the water getting into it