A- Simple for FRSky transmitters, one gimbal for both sides. Replacements are ~$12ish. Can be self centered out of the box too. (not sure how much 9XR gimbals are)
B- All hobby grade transmitters should be able to use these boards as long as they have PWM output. Some of the newer boards like the Open Panzer and Clark can even take advantage of Sbus.
C- Both the Taranis or 9XR can use rechargeable. The cheaper Taranis comes with a AA battery holder but that can be removed to use a rechargeable battery. I think the 9XR is similar, my 9X used the AAx8 config when I got it.
D- That is dependent on the motherboard but all the current boards out have one stick throttle and turning. Np here.
E- Once again dependent on the motherboard.
F- OpenTX which is available for both these transmitters offers one of the best if not THE best transmitter OS there is. If it can't mix it I don't think it can be done
Most likely if you are looking at something like the TK22 with 4ch operation then yes you will have to do lots of mixing but yes it is totally possible to get most functions off that stick. However you might be better off spending a few bucks more for the 8ch version or looking at one of the other offerings from someone like IBU. These might effectively use more than the 4 channels than the base models of these companies offer. If you are looking to get all the functions off the sticks and not looking to do the mixes than the higher end models might be something worth looking at. Personally I would spend the extra $40 for a much newer and more reliable radio with parts available from US sources (Aloft Hobbies has parts and is the official US repair center). My co-worker actually just upgraded from a FS-i6 to his QX7 and loves it.