The signatures aren't at all close to authentic counterparts. Whoever forged this was pretty lazy too, using the same pen and writing style. Even if he'd done a better job faking the signatures, this is not an easy set to complete and nearly impossible with the exact same pen. Most of these actors don't do conventions, so the pristine nature of this makes little sense. I don't think Rickman signed much, if any Potter items.
I'm guessing this was really cheap.
That price is a dead giveaway. An authentic piece with those signatures would hundreds more. $5 is too much for that junk.
The only member of that cast I've met is Felton, and I have no idea what that forger was trying to do there.
Not really sure. If you join this group, you can ask - there are some pros there who tried over the years (a couple succeeded). https://www.facebook.com/groups/realautographcollectorsclub/
I'm not super well versed in Rickman, but that's decidedly closer. He really didn't sign much HP stuff - I've heard most collectors say they couldn't get him to do it. Not that he never did, but it was especially rare. If it was me, I'd ask questions to the seller about how he got it, since it was something of a feat. Who's selling?