It should be possible, I have never tried it though. The first step should be to make space for root partition for BT4, therefore shrinking Mint partition. As for the swap, I think it can be mutual...

Disk_partitioning

I mentioned that you prepare D partition in Windows, not in BT4 installation setup. That should be done by splitting D in 2 parts, so that would give you an extra E drive which you should size...

that is strange; i have exactly the same card and i cannot complain. I am noob too, but packet injection with aireplay worx just fine.
airmon-ng check wlan0should give you some hints too.
IMO,...

From my experience, it's best if you prepared D drive in windows first.
That would be:
delete whole partition

create partition in the unpartitioned space [say 90% of space]
create another...