1) i don't understand the point. the self-test it's about working over the internet. "localhost" is not even for working in your lan, it's only by your own. so they are totally different.
2) the IP you choose has no effect on other people. it's for your convenience, to copy&paste the correct url, or rather the one you are going to use.
since you are going to work with people over the internet, you'd better choose the external one.
THEN, it won't work if you will give that same url to people in your LAN.