Should a wicketkeeper be fined for appealing when he knows there wasn't an edge? A bowler for appealing when he knows it was going down leg? An umpire when he gives a batsmen out when he wasn't?
Should spinners be banned for consistently trying to influence the umpire by appealing for absolutely everything?
Yes the keeper and bowler should be fined. The key word is "knows". Since the word "knows" is absent from the other two questions, therefore they are cases that should not attract fines.
How do you know he knows? Well, assuming he doesn't admit/boast about it, you could still have a review process to determine did he or didn't he, although the standard of proof required would need to be quite high (something like 'beyond reasonable doubt')