Is it true I can go back to Vault 101?
If yes then please let me know (with minimum spoilers) what things I need to do to be able to go back and check things out.
And if I aim for multiple targets in V.A.T.S. and the Mysterious Stranger appears will he just kill one targer or does he shoot all that I am locked on?
One last thing, Does having Dogmeat with me lower the rate of the Mysterious Stranger appearing to help me?
Sorry if there is a wiki that covers this but I can't locate it and I think it would be better to get advice from gamers directly.
Yes, there is a wiki. But don't use it! It has ruined the gaming experience of so many people by having explicit spoilers even in the most innocent articles.
On questions:
1) Once. As a general hint, visit Megaton after you have made first contact with the game's villain and look at your list of radio stations.
2) I believe he can appear only once per VATS session, but I'm not entirely sure.
3) No. Dogmeat is a companion just like anyone else. A normal NPC just scripted to follow you under the right circumstances. Mysterious stranger's appearances are handles by completely different scripts.