Galadriel specifically states that she gave it to Gimli because of the way he asked, adding the fact that she had commanded him to ask for what he wanted as an afterthought. It was also obvious that Gimli had a gigantic crush on Galadriel (who can really blame him?), this was probably very flattering for Galadriel since Dwarven men are usually only interested in their own kind. I think it was a combination of these factors that led Galadriel to give Gimli her hair.
As for the subject of why she gave none to Faenor it says in UT not only that they were unfriends forever but it goes on to say that she had to some degree forseen that Faenor would eventually lead to the Noldor to ruin if he were allowed to. This would obvisously not dispose her to giving much of anything to Faenor, plus there is the previously stated fact that he was a very greedy and creepy dude.
P.S. I will post the part where Galadriel says specifically why she gave Gimli the hair later today I am at school right now and do not have the book on me.
Dondagnirion
"There is no spoon."
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"It is useless to meet revenge with revenge; it will heal nothing." - Frodo
"Will shall be the sterner, heart the bolder, spirit the greater, as our strength lessens."
"The only reason for time is so that everything doesnt happen all at once." - Albert Einstein
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