What is the error returned by BiCGSTAB? It's description says "the tolerance error reached during the last solve". Is it the norm of the residual? I tried calculating the residual norm based on the solution, I get a different value.

It is the relative residual error, it should be close to: |Ax-b|/|b| (it might be slightly different because |Ax-b| is not explicitly computed but quickly updated at each iteration.

Is the tolerance that is specified as a stopping criterion also the magnitude of the relative residual?

yes. I'm updating the documentation to clarify these questions.