Is the toll being paid in both directions (in and out of SF) ?

And that is the case for all bridges, not just the Bay Bridge. Only SF-bound (or West-bound, in the case of San Mateo and Dumbarton bridges) drivers pay.

All bridges are only going INTO SF.

No, only going into San Francisco.

1 way...pay only goint to S.F.

One way toll

No, yo don't have to pay while going from SF..