Yes you can use that exploit.
Yes you can use a Wii controller (where does it say to use a gamecube controller? I see no mention of it).
BootMii does not depend on your System Menu. It depends on a piece of code called boot1 which will never change on any particular Wii (it can't be updated by Nintendo). If you have an old Wii, you can install BootMii as boot2. If you have a newer wii, you cannot. HackMii Installer will tell you whether or not you are able to install BootMii as boot2. Regardless you can always install BootMii as IOS, and in actual fact the HackMii Installer will automatically do this as soon as it is launched. (Note that BootMii as IOS has NO brick protection)
No you cannot use a flash drive. You MUST have an SD card. Brawl cannot read flash drives, which should make it extremely obvious that this exploit couldn't work with one.