Note: This is an AmE perspective (BrE is different, see comments/other answers)
Crowd is singular. Crowds is plural. You can't use crowd plurally, you have to use crowds if you mean more than one crowd.
Verbs work the opposite of nouns, verbs that end in s or es are singular third person and verbs that don't are plural third person. (Anything not third person uses the form without the s or es).
So it's always crowd believes and crowds believe.
Nouns that describe a group of X as a whole are singluar, if they refer to one of that group. If there are multiple groups of X, then plural is used.
I don't know where the pile of papers is (pile is singular because it refers to one group of paper)
I don't know where the piles of papers are (there are two or more stacks of paper)
I think it's technically wrong, but you might hear something like this where a plural pronoun is used. I'm not sure whether referring to a virtual "all of the papers" which can be argued to be implied is totally wrong here.
I took that pile of papers and threw them in the trash.