Can I Use It on More Than One Computer?
Yes. The unlock is tied to your purchase, not to a single machine.
Yes. The unlock code comes from your purchase, so you can use it on your desktop and your laptop, and again after you replace either of them.
It is worth keeping the email with your code. It is the only thing you need if you reinstall, and there is no account to recover it from.
It runs on your own computer and is free for your first 500 photos. Unlimited is $9.99 once, on macOS, Windows and Linux.