Last first, you can certainly handle carp on a 3 wt rod, and I've landed some dandies on a 2 wt. The amount of pressure you can put on a fish is a function of the tippet strength, not the rod weight rating. Remember that in situations like this you always want the tippet to be the weak link, not the rod.....
Dt lines come in floating, these days that's about all you can easily find them in (when you can find them).
A 3 wt. is an ideal trout rod unless you are going to be pitching large streamers or heavy nymph rigs long distances....and a 2 or 3 weight is perfect for 'gills and small bass.
It Just Doesn't Matter....