1.   As for the ceiling, sand it enough to reduce gloss and roughen the finish, and apply a latex enamel undercoater.

2.   But to repaint, sand the finish as thoroughly as necesary to remove any loose paint, roughen the finish and reduce gloss.

3.   Does it make sense to roughen the finish and do another coat?

4.   First, sand it to reduce gloss and roughen the finish.

5.   First, sand the legs heavily with medium sandpaper to reduce that gloss and roughen the finish to enable the primer to stick.

6.   If it is vinyl-coated paper, use fine sandpaper to roughen the finish and reduce gloss.

7.   If that test patch of varnish peels or lifts, you will have to hand-sand to roughen the finish before varnishing.

8.   If there are bare wood areas showing, sand the entire floor lightly, to reduce gloss and roughen the finish.

9.   If the slide is fiberglass painting it is easier, but the finish must be roughened, and all the caveats that apply to PVC also apply to fibgerlass.

10.   It will not hurt to roughen the finish and add one more coat of varnish.