Yes, they do have Ferrari engines as well as other Ferrari components.
It will be interesting to see where they land competitively. I think Romain Grosjean, their lead driver, is extremely talented and given a good enough car, can win races for them. It would be great if Haas can be competitive with Williams in their first season. I kind of doubt it.
This season will be have many interesting story lines. Haas's arrival in the sport is one. Renault joining as a constructor instead of just an engine supplier is another. Seeing if the storied McLaren/Honda partnership can, in it's second season of being reunited, become competitive is a third.
I believe that Mercedes will probably dominate once again for 2016. If we're lucky, Ferrari will have closed the gap to Mercedes even more. And despite the relative weakness of the Renault engine, Red Bull can never be completely counted out. They were definitely closing the gap towards the end of 2015.
2017 may be all kinds of different, with the formula spec being modified substantially to improve the lap times. Can't wait.