Hi!

I´m not sure how many systems can an active player activate during an tactical actions.

Only one system or a various number of systems during one tactical action?

general rule of thumb is that you can activate one system during each tactical action. This can be modified a little by one of the technologies (forget the name atm) or by using the Transfer action. But in general, activate one system per tactical action.

Yup, just one system per Tactical action, though you can make more than one Tactical Action per "round" (ie, one Action Phase). You do them one at a time, and have to wait until your next action to do a second one, but as long as you have the Command Pool counters to activate systems, you can end up activating many systems.

Transfer Actions allow you to activate 2 systems, but note that there are some differences between them and Tactical Actions, and are more restrictive in how they can be used.