As the above post mentioned, you don't need the Trucha Bug to autoboot legit games; only for those discs that require the trucha. Essentially, you're going to need to config the discs to autoboot before you burn them. There's a program that does it automatically, but I never had any luck with it. There's also a way to do it manually using BootMe, which worked for me. Check out this thread for further details: http://www.wiihacks.com/bricked-wii-...-can-i-do.html
And no. If it is configed to autoboot on another wii, it'll be configed to autoboot when you move it.
Try burning a disc first as it may be set to autoboot. My wiikey was shipped set to autoboot, and I didn't request for such to be the case.