The fire damper is connected to the power supply. I tested the fire damper manually (by pressing the test button), but it will not open when the management system tries to bring it to the open position. Is this normal?

Yes. After a manual test, the actuator must be activated again. To do this, you should hold a 9V-battery briefly against the contacts in the battery compartment. Thereafter, the permanent power takes over and brings the blade further to its stand-by position (open).