I'm just going to assume you're talking about an external usb drive?
Unless your system supports booting to a usb device, then no, you won't be able to boot from it.
Enter cmos setup (bios) and go to the boot section to see if usb is in the list of supported boot devices.
It's possible the info may be in your manual as well.
I have a somewhat older IBM laptop that can't boot from a usb device.
I use an external 2.5 drive enclosure that contains another drive compatable with my current notebook.
If my old drive pukes, I just take the backup drive out of caddy and stick it in my laptop.
5 Minutes and I'm on the new drive.
Backup software is a matter of preference. I don't trust the MS backup utilty as I have seen problems with it.
I prefer Acronis or an older version of Ghost.
In any case, glad to see you take backup seriously, too many people don't.