it depends on what make and model your BMX or MTB is
A racing bike, a mountain bike and a BMX bike.
It's a BMX intended for "Street" style riding. Heavier and stronger than a race bike, but will probably have brakes as opposed to a bike for "vert" riding.
Depends on what type of riding you want to do. For BMX-type stunts - get a BMX. For going some serious distances both on and off-road - get a MTB. Don't really know what you mean by jump bike.
Yes, if you can find the correct bottom bracket for the frame.
There are MTBs with 20" and 24" wheels for smaller riders, which probably is the closest thing to what you're describing. These wouldn't be BMX bicycles though, since BMX bikes don't have gears and have a taller handlebar than a mountain bike.
BMX are built around 20" wheels while MTBs are usually built around 26" wheels.
It will if you have bmx (or bmx style) cranks.
It's more a question of "different" than outright "better".If you want to use your bike to get around with, then a mountain bike with gears and bigger wheels is better. It will be faster, less fatiguing and offer greater rider comfort.But if you want to do BMX style riding, with jumps and tricks and that, then a BMX is a better choice.
No such thing. Trials is a sub-sport of mountain biking, often called "mountain bike trials". It's a sport similar to motorcycle trials where one takes a light bike and hops around an obstacle course. You might have heard "BMX" and "trials" in the same sentence because a BMX bicycle can essentially make a good trials bike with minimal modifications.
Probably not. BMX bikes usually have freewheels while MTBs usually have freehubs, and these don't mix. You might be able to use parts from a single-speed MTB on a BMX though.
Not necessarily, but if you want to get into serious tricks like tail whips and bar spins i suggest you get a bmx. but you can easily do a wheelie or a small bunny hop with a mountain bike.
You're probably thinking of "Dirt riding" or "Dirt Jumping".