How to relate the counter torque of a generator with its speed?
For your second question  - generally - yes. Constant speed means no acceleration. Acceleration is proportional to the torque. Acceleration zero means torque (sum of total torques) zero. As for the first one, you can use an energy equilibrium equation:
 $$E_{electrical}=E_{mechanical}$$
$$E_{electrical}=V\cdot I$$
$$E_{mechanical}=\tau\cdot\omega$$
Plus applicable loses. Here V and I are voltage and the current, tau and omega are the torque and angular velocity.
(Well, strictly speaking these are not energies, but power, but since we are interested in a momentary values, the equality still valid).