I don't know about the other issues, and couldn't without seeing. But what you describe with front cage rub is 100% normal (within limits). The cage has a certain width, and in any one position that won't be enough to allow for the chain to come from both extreme angles. Normally the FD is trimmed so there's no rub in high gear with the chain coming from the outer two thirds of the cassette, and the inner ring with the inner two thirds. So the middle of the cassette should be rub free with either chainring.

On certain bikes it's possible to be pretty much rub free with all but the most crossed combinations, but that's rare. The fix is built into better FD levers which have an extra fine tuning click to move the cage over slightly to prevent rub when riding crossed combinations. Yours may not, so it's a matter of getting the best adjustment possible, and living with the limitations.