A prank call is a practical joke made by a child or childish person, usually out of boredom. There's some humor involved-- though not always for the person targeted.
A crank call is a type of prank call where the person is old enough to have better ways of entertaining himself, or is motivated by pathology of some sort. Crank calls aren't funny, and usually they're intended to be scary-- or antagonize in some way.
A kid making a prank call will target no one in particular, usually, and ask a setup line like "is your refrigerator running?" If you're duped into saying yes, you just made his day-- and he says "well you better go catch it!"
A stalker or malicious gossip making a crank call usually knows who he's calling, and doesn't like that person. "Do you know where your wife is right now?" is the kind of thing he'll say, and then hang up. Or single women will be called by a perv who doesn't say anything, just "breaths heavy" and delights in any annoyance or fear he causes. Iago might call Othello and hang up without saying anything, to cause suspicion-- the idea being that the call was for Desdemona, and Othello wasn't expected to answer.
Bart Simpson call's Moe's tavern with pestering "is Mike Hunt there?" jokes, and Moe calls the name out and gets ridiculed. That kid's a little wickeder than most, so his phone calls are in that grey area where prank becomes crank. If he's still doing it later in adult life, and it's still Moe he's plaguing, then Bart has evolved into a crank caller.
Well, it's like I say-- there's a grey area between the two. Also, the difference can be one of degree, with the prank call being the more general or normative term and the crank call being a more extreme form. But people who draw a sharp distinction between harmless "humor" and the malice of telephone harrassment would see the two in terms as I just explained them. I wouldn't be surprised if someone didn't pop up and argue the idea that you can use either word to mean the same kind of annoying behavior.
I don't know of a separate verb for making prank phone calls. I would just say "to make a prank phone call".
I have never heard the expression "crank phone call" before now. I would have assumed it's a made-up word meaning a phone call an old, cranky person would make to complain about something. Whenever a person calls somebody up as a joke I'd say "prank phone call". I always leave the word "phone" in too.
(I'm a native English speaker from the USA)