Mosquito fighter/bomber

The Mosquito fighter/bomber had rather exceptional performance for an
aircraft of that type. Even faster than the early Spitz! It was fast with
relatively long range and was used as a pathfinder, night fighter, recon,
and insurgent bomber. Was it ever considered as an escort fighter for the
daylight American B17's?
How would it have stacked up to a ME109? Stukas were used to break up
formations of B17s. I would think the Mosquito would have been effective at
least against these, as a fighter. Was this ever considered before the long
range Mustang took over this task?