Small back tire better worse
 

I have a montain bike fairly custom 18 speed and the Front wheel is 26 inch and the Back is 20 inches does this give me an advantage. I think so I go really fast especially compared to the previous size back tire

You will be able to accelerate more quickly, but the larger the wheel, the more distance you will travel in a given number of pedal strokes.

DEMON

There also seems to be less friction with larger tires especially off road.

Joe

Well one downside is my bike is lower to the ground and turning is messed up. For Example if the side on which I am turning has its pedal down it hits. Stamina is also a problem over long periods of time the smaller wheel takes more energy. I'm tring to figure out a way to weld it so the pedals will be higher also to put brakes on the back. But overall small back wheel good, bad?

20" seems a bit extreme, how about a 24".. I think there would be benefits and drawbacks.. You will have to push harder gears, or pedal at higher cadence to go the same speed with smaller wheel but you will be easier on getting up to a given speed since less mass, the 20" will not roll over obstacles as easily..

You could always go disc brakes then you could use whatever sized wheel you want.