Should I remove chipped lead paint from door frames or seal and paint over

I honestly do not think painting a floor would be a good idea. A solid color paint or stain will likely chip and wear unevenly. As in wherever your high traffic areas are will look awful in no time at all.

If you are to paint it you will need to sand the gloss of the previous coating. This glass will prevent any other paints or stains from correctly adhering to the surface. The same exact rule applies to painting a glossy wall or any other surface.

Definitely read up on the EPA 'renovation repair and painting' rule.

Option #3, the 1/4" drywall, is likely to produce the best and cleanest results, at the cost of loss of room space and alteration in the look of all your trim. You'll have to extend all outlets also. Of course that sounds suspiciously like what happened last time. Eventually your room will be solid wall covering with no center.

Option #4 sounds attractive if that texture on the wallpaper will really hold the joint compound. I'd run a test with and without the primer/sealer. Remember worst case here it cracks later and you redo it all with #3.