I am not an art conservator, but there are some common sense things you can do here. If you want to put the fabric under glass or acrylic, I would use a shadow-box approach or at least a spacer between the glass and the fabric. I don’t think you want the painted fabric touching the glass.
I would personally wait at least 6-8 weeks for the paint to dry before framing a piece. Paintstik oil colors are oil-based paints and they take longer to dry than water-based paints. Better safe than sorry.
For a definitive answer to this question, I would contact the art department at a local college or university or consult with someone at an art gallery that handles oil paintings.
