This is the continual debate, but the theory is as follows:
1) Special abilities are not essential.
2) No, they are not irrelevant. If the right players have the right SA then they can be very useful.
3) It depends on if you can get them/develop them on the player. Don't try and put an SA on every player you buy. The best players to put an SA on are the Youth graduates, and 18yo players from the Transfer Market if they are Fast Trainers (if these exist any more). And put the SA on after you put an extra position on a player (if you are going to), and before you train up the player's Quality.
4) There are SAs which should work better depending on position, eg GK (1-on-1 stopper and Penalty stopper); Dx (Aerial defender, Defensive wall); Mx (Dribbler, Playmaker - these are particularly useless, IMO); AMx (Shadow striker); ST (1-on-1 scorer). Corner kick can be put on any wing player (xL or xR) with good crossing skill; Free-kick and Penalty kick on any forward player (AMx, ST) with good Shooting and Finishing skills.
The effect of the SA is to give an extra star performance in the particular area the SA is aimed at, e.g a 4* striker with Penalty kick SA should have the chance of scoring a Penalty that a 5* ST would have.