Use Aluminum Foil to Glue Down Loose Vinyl Tile - Place a sheet of foil over a loose self-stick vinyl tile, and press a hot iron over the foil until the adhesive backing melts and sticks to the subfloor. (this old house website)
Stains occasionally bleed up through vinyl floors, and may have several causes, including chemicals in the adhesive. Here's how you can tell if this is what's causing the stain and what you can do about it.
26 reasons to hire someone else Hardwood Floor Sanding: Do It Yourself Tips. 26 tips for a smooth job. (This may come in handy after the remodel since we plan on doing real hardwood floors throughout the house instead of this crappy laminate stuff)