1. I'd agree.
2. Make a folder on the other drive and chown it to yourself and your default group. For example, if you have the other drive mounted on /mnt/backup:
Then set /mnt/backup/buzzingrobot as the target for your backups. I do this and it works well.
$ sudo mkdir /mnt/backup/buzzingrobot
$ sudo chown buzzingrobot.buzzingrobot /mnt/backup/buzzingrobot
Your username might not be buzzingrobot, but you get the idea.
3. For the type of use you suggest, I think you want something like CloneZilla or, if you want to get your hands dirty, dd from the command line. Others may have better suggestions.