I'm new to android. My old dumbphone broke, so I thought about buying a new smartphone (Android).

I've been reading about rooting the phone, but I have some concept doubts: when you buy an Android phone from a carrier, you don't have "root" access. When you start your phone, does that mean a "user" account (like I have on at Linux/Mac, '/home/myself') is used? Does '/home/myself' or similar exists in Android phones?

If I "root" a phone, will I start the phone as root when I turn it on? Will all applications now run as root? Can I define which apps should have root access?

Since Android is a Linux, I'm interested in having access to a terminal and some unix utilities (ssh, rsync, etc). I don't mind having to use a bluetooth keyboard and vi (to edit /etc/hosts for example) if needed. Is this possible? Can I have a terminal with a lot of unix utilities (I know busybox is available)?

If Android is essentially a Linux, to backup my device, shouldn't I just be able to connect to root it, do a full `tar -cvzf /` and them a scp to somewhere? Why would I need to have Nandroid and these full blowns solutions?