Well it depends whether the point of the debate is to establish the truth or to win, to prove you are right. It can be a subtle art in convincingly arguing for something you do not believe in.
But fallacies dismiss a particular argument, not what is being debated.
Argument A comes, you need to combat it. It can either be with a counterargument or by proving the argument is a fallacy. Either way works. Last argument standing wins.
Not really, in the end 90% debates (figure comes form a poll of 3 people i conducted myself) end with participants convinced they one and the others are morons.
Oh, absolutely. The aim of the conversation matters for sure. Arguing for something you don't believe in, otherwise called "Devil's Advocate" argumentation, is a great art in trying to see if you can really find flaws in opposing views, but I think the intention of the person is sometimes portrayed as a desire for the truth when it in fact is a desire to be against the grain just for the sake of it.
I for one think that there is more value in having the aim always be pointed at "is this really true or not?" rather than pointing it at "can I find all my opponent's fallacies and point them out?"
And yes, fallacies SHOULD be recognized in order to dismiss a particular argument, not WHAT is being debated, that is the proper approach I think, and yet people fall into the pit of COMPLETELY forgetting the goal (to figure out WHAT is true or not), in the aim of appearing to be the "more right" one.