can I put bead board over popcorn ceiling
You sure can.
You can! You can also use prefabricated ship lap! I used ship lap in my small bathroom. It looks beautiful! I like is so much better than the ugly old popcorn!
Yes. That is often a better solution than removal of the popcorn for two important reasons. 1) popcorn is messy. 2) some popcorn ceiling contains asbestos and leaving undisturbed and enclosing it is safest.
In some cases the "popcorn" will need to be knocked down a bit before applying any other larger panels.