At some comedy clubs, is taking videos against the policies?
yes. the rules.
Yes, mainly due yo copyright and intellectual property of the comedians; sometimes its also due to commercial agreements or restrictions.
absolutely, yes. videos can be duplicated and given to others who haven't paid anything. Thus, every club I've ever been to has a strict no videos policy [except for the management and whomever they agree with the performers to give copies to -- scouts and agents, mostly]
Yes, and the explanation is it’s against policy which is typical for many performances, the venue makes money from attendance and the material is often copyrighted and not for use outside the show.