The Mesa F-50 is based on the Studio .22 pre-amp design from the early 80s - a great sounding, but somewhat noisy amp. Randall Smith spent a significant amount of time trying to get this design quiet enough to use with a 6L6 output section, and the F-series is the result.
Although the background noise level is a little higher than some tube designs, it should definitely not be distracting. On the clean channel, my F-50 is very quiet. I get a little noise on the dirty channel, but not enough to compel me to try different pre-amp tubes. It's worth mentioning that a lot of owners have mentioned good results with trying different pre-amp tubes to reduce noise. The Mesa help desk will instinctively set expectations that tube amps can be noisier than other technologies, however, the noise levels (even on the F-series) should be low.
The fact that you're noticing volume variations as well, makes me wonder if your Power amp tubes are also failing. If I were you, I would try another unit, and see if it exhibits the same problem. I suspect a good set of tubes might solve your problems.
I have no problem using my F-50 for recording and TV sessions (I have some clips over in the Rigs and Tones forum if you're interested). The only time I had a noise issue that impacted a session, was when I had an old Multi-FX unit resting on the combo, and there was some emissions intereference caused by the Multi-FX rack unit. Don't forget to use good quality cables (another potential source of noise).
I'm sorry for the trouble you're having - not the most stress-free introduction to Mesa. I hope you find a quick solution, and like me, end up having a fantastic experience with the F-50 (my favourite amp from Boogie)!
Big smiles,
Andy.