Install Android-x86 in Virtualbox VM, then root it
For your reboot problem, it sounds like your boot order is booting off the .iso, i.e., cdrom, before it looks for the disk partition where you installed Android. Shut everything down and disconnect the .iso. You can just delete the CD device under the controller within VirtualBox Settings->Storage. You probably shouldn't just change the boot order or you will have trouble reinstalling if you ever need to. However, if you want to change the order, look under Settings->System->Motherboard.