Not really.
If it's meant to be a race bike, gears are not allowed. If it's meant to be a dirt or a vert it won't have them, partly because gear hubs are more easily broken and those bikes will get thrown around a lot, parrtly because there'll be some tricks that can't be done on a geared bike.
It is possible to buy geared bikes that look like BMXes, but odds are they won't hold up well to proper BMX use.
It's a bit of a strange combination too. BMXes aren't built to be ridden long distances in varying terrain(you can't sit and pedal very well). And geared bikes are meant to be good at exactly that thing - longish rides in varying terrain.
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.
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.
I have no idea what you mean by "gear bike", so the question can't be answered.
It will if you have bmx (or bmx style) cranks.
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.
Two, but this is not the same as how many speeds the BMX bike in question has. A BMX bike has a sprocket in the front, and a cog in the back and each is a gear, but is considered a single speed bicycle because two gears and a chain are required for transmission of rotational force from the crankset to the rear wheel.
you can find a BMX bike in halfords
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.
As a general rule if two bikes are in the same price range, the smaller of the two will be lighter. This because there is less material used in the smaller BMX due to it's much simpler construction. But, when you head for the high end, a flatland or racing bike is going to be much lighter compared to a mountain bike.
The bmx thruster rampage bike is a exellent bike
One can buy a custom BMX bike in Las Vegas from a few stores. One can get a BMX custom made from 'Just BMX', 'Bolder BMX', 'Bike World' and 'Vegas Bike Store'.