Unfortunately there is some misinformation in here...
No you cannot use the stem from a bmx bike, yes the steerer tubes may be the same size, but generally, mtb handlebars have a much larger diameter then bmx bars, and will not fit a bmx stem. There are a few options bmx sized options, but not many.
Your seat post diameter is whats going to matter, and unfortunately, bike seat tubes come in a wide range of diameters. I believe the most common bmx diameter is 25.4mm,and mtb ranges from 25.4 to like a 31 or something.
Pedals will fit any bike, bmx or mtb, I ran bmx pedals on my dj, as do most people.
Hubs, the axle size is not really an issue, unless you have a 20mm fork or a qr15. Bmx runs 12mm axle for the most part i believe, mtb can run a couple sizes, but I think it's 9mm you'll find most common. What you need to worry about hubs is the spacing, bmx is 110mm, whereas mtb is 135, and 150mm on some bigger downhill bikes.
Brakes are up to you, discs are stronger, aren't affected by bent rims, give better braking power in general. But it depends what you plan to do. Another option is hydro v-brakes, but they are more designed for trials riding. Get a good set of mechanical discs, avid bb5' or 7's are great, and aren't going to break the bank.
For jumping, get a good set of bmx cranks, with a micro drive, 2;1 gear ratio, that's all you'll ever need on a dj. That means singlespeed. Ballpark micro drive would be like a 24 tooth up front and 12 out back.
Brakes are up to you however many you choose, if you're just starting, I recommend both, as it's a bit safer, as you get better you may choose to get rid of the front to free up space for spins and such.