We have used it on cork coasters, rocks, small clay objects, objects of unfinished wood like small boxes and picture frames, paper mache letters, other kinds of paper, fabric and more. 

This paint will not work well with materials that are not absorbant, like ceramics, plastic, glass and anything with a waterproof coating.

Because the paper absorbs a lot of liquid while it is painted, it can indeed warp a little. This is normal, and it can easily be fixed. 
One solution is to flatten the paper under some heavy books (after it has completely dried, so you don’t stain the books) or you can iron it flat on medium heat with no steam.