I think you should be able to install all of these on separate partitions on your USB drive if you want! (If I'm wrong, someone will correct me
) Note that the boot loader will be installed on the USB drive so that if you try to operate your system with it disconnected, it'll hang as the boot file on the system's internal disk's mbr will be pointing to the usb drive.
32bit, 64 bit? Depends on your processor, not the disk.
"Will it get hot?" Does it get hot at present? There shouldn't be any noticeable difference, they usually keep spinning once they're plugged in.