wd40 or tar removal
yes you need something more abrasive than cleaner wax (which contains slight abrasive)
meguiars ultimate polish/compound would do

waxing doesn't remove scratches. and you might want to get something that might last longer on our climate. ultimate wax is good
most carnauba won't last more than a month.

tips given by my sifu

cracks
Saturate paper hand towel with tar remover
Place on whole film.
Cover up with a plastic sheet.
Tape up.
Remove after 10mins.
Use a towel to gently remove "disintegrated" film off headlights.

Yellowing.
Saturate paper hand towel with tar remover and tape up with plastic sheet at an edge of film.
Remove after 10 mins.
You'll fi d the film coming off. Lift it up and spray a little more of tar remover.
Get a good grip of film and gently peel it off in 1 sheet.