Other people have answered but nobody has actually given reasons this is done/not done so let me relate my military police training:
First, yes to all of your questions with a bit of a caveat: there are small hammer and hammer-less guns which prevent blocking the hammer (see pg. 3 and 20 of police tactics document) so only option there is cylinder2 or slide.
Now for what officers and military teach for this situation:
Gross-motor skills are limited in "fight or flight" situations (pg. 14). So reaching, grabbing, and trying to stick fingers or remember to hold a weapon "just so" are not skills you want to rely on. What we do teach is to use your elbows and knees and grab the weapon with both hands. Part of the reason is that if I have both hands on the weapon I at least have a chance to stop the slide, hammer, or cylinder.1
Use improvised weapons - for officers this involves getting them to know that "if I have a heavy radio/clipboard/pen it will hurt when I swing it" (pg.9-11). So the tactics would be more to ensure the muzzle is not pointed at you - again with gross-motor skills this involves more of a push or grabbing the wrist for better control - then bashing the suspect with whatever you got or even just throw stuff at him to distract and confuse so you can either get away or get in close. In fact, we advise against grabbing the actual gun3 because if it does fire - your hand will now be damaged (burned or "bitten"1).
So yes, yes you can stop the hammer, cylinder, or slide and have a handgun not fire but if it happens it would likely look more like the above than anything like hollywood shows.
Police Survival Guide, Police: the law enforcement magazine
1 Search for beretta bite if you want to know what that pain looks like
2 There is a story in Ip Man's biography (and portrayed in the movie from it) that he once knocked the cylinder out of an old (pre-WWII to WWII) revolver - unknown validity
3 At this point, the idea would be once the suspect is in pain/distracted - then try and take the gun using standard hand-to-hand techniques. However, I've actually seen another officer grab a suspect weapon when doing this and manage to both stop the gun from firing and pop the magazine out (he admitted it was dumb luck, surprised him as much as suspect, but it happens)