paint the plastics by sanding them down with 180-220 on a DA or by hand. you dont have to remove all of the texture, just about half of it.
clean the part and soray an adhesion promotor, followed by two coats of primer. sand the primer down with 400 grit and re apply adhesion promotor where needed and reprime the whole piece. Be sure to use a flex agent in the primer since you are working with plastic.
final prep the primer with 800, seal, base and clear. again, adding a flex agent in the sealer, base and clear.
as far as painting chrome. spend some time with some 80 grit or an pneumatic air grinder with a scotchbrite attachment to scuff the chrome as much as possible. House of Kolor makes a great adhesion promotor that i have used on chrome stuff for years with no issues.
prime, block, prime, finalsand, seal base, clear.