I always meet up with dogmeat while it is fighting with 3-4 raiders!
will there be any chance those raiders kill dogmeat or dogmeat will always win? what is the raiders kill the dogmeat in that fight. will I still be able to ask dogmeat to join?
is it true dogmeat will always heal itself a bit in HP after every fight?

The fight is scripted, the raiders have very very low health so Dogmeat always wins.
And if he would have died, I don't know how you could have asked him to join you.

Dogmeat, like every companions, automatically fully restore their health after each fight. Dogmeat is not very resistant, though, and can get in your line of fire since he charges the ennemy without remorse.

By the way, that goes in Fallout 3 General Discussion.