I am designing an online game in which server records the shots, inform players and pass turn. Can I consider Server as an actor or it should be a part of my system?
Shortly your server is a part of you system
As for identification actors itself you should answer for next questions:
So users (players, admins and so on), external sources (ie used external API) are actors definatily in your case.
Server can be an actor. Here is an example. As you can see server is out side of system.
It can be difficult to idenify all actors immediately but you can revise your use cases (and actors) during creation system.
Given from source
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