Depends on the bike frame..
No. a 9T sprocket will only fit a cassette hub, and not freewheel hubs.
Probably. Today BMXes can have either a freewheel hub or a cassette hub, but as long as you stay within the hub type you can move parts from one bike to another.
Kinda, sorta. You can certainly (have someone) build a BMX wheel around a fixie hub. I suppose you could somehow disable the freewheeling action of a regular hub too, but I wouldn't recommend it. Putting back pressure on the pedals on a bike that hasn't a real fixie hub can cause the sprocket to unscrew.
You need the right kind of hub for that. If you haven't, buying a new rear wheel - with the right kind of hub - is probably the sensible option.
Yes you can.... you can put any hub, spoke, and rim combinations together...maybe a few ecceptions but you can deffinetly do that... just bring the parts to your local shop and have them lace it.
It'd be a fairly strange BMX if it has a gear shaft. Most "real" BMXes are single speed, their driveline consists of cranks, a bottom bracket and the rear hub. No gear shaft there.
If you have a flip-flop BMX hub, you can put a 14T on the smaller diameter side of the hub. If you have a cassette hub, you can get as small as 11T.
I'd say no. It has suspension, which makes it heavy and sluggish in handling. It also has an externally geared rear hub, which is likely to get banged up real quick during the kind of use BMX bikes usually have to put up with.
There's too much room for personal preferences for there to be a solid answer to that, it's like asking for the best candy, or best band.
Depends on what you mean and what the different bikes are like.If you really mean hub:The hub is the center part of the wheel, that holds the wheel axle and the spokes, and in some cases the brake rotor.Most 26" MTBs these days use dic brakes, while BMXes mostly use rim brakes. And to be able to fit a brake rotor to the finished wheel, you need to start with a disc brake hub, which a BMX hub is unlikely to be.But using a rim brake BMX hub to build into a rim brake MTB wheel - no problemAlso, most MTBs use 32 spokes, while for BMX, 36 spoke is more common. You need to match hub spoke count to rim spoke count to avoid complicated builds.If you mean wheel:BMX regular size is 20" against MTB regular size 26". You'll get all sorts of troubles by dropping 6" from the wheel diameter. The bike will handle differently, and the pedals will drop a lot closer to the ground.
change out the hub