First question. what weight of rod should i use:
I would go with 7 wt minimum
What flys should i use: Carp are strange, some days they will eat anything, others nothing. But I have caught them on an Adams and I have caught them on a wooly bugger and nymphs.
What: fish should i target: If they seem to be doing nothing, I usually ignore them because you can spend a day casting to them and do nothing but spook them a bit. If they are tailing, they are feeding off the bottom or at least subsurface. If you see them slurp something fromm the surface you have a decent chance of getting a dry fly bite. If you have moving water cast as if they were trout and if in still water cast to where they seem to be headed and let the fly just sit there.
What size of tippet: I would try not to go below 8 pount test, but if they continue to shy away from you. try 6, just know you need to work them real easy. Now for nymphs, as big as you can get away with... 8 to 10 test.
Hope that helps