You do not have to re-clear customs/immigration to do it on 2 separate tix. I just did JFK-FCO/FCO-MLA on a 2 tix and 2 airlines (DL/AZ) and they even checked my luggage all the way through.

As long as you are continuing through an international connection, you won't have to clear. Most airports, especially the big international terminals like FRA have terminals set up for connections like that.