So if I use an order card that activates both a necromancer and a reanimate and then get results for the Influence ability for the necromance can the reanimate attack twice?

Yes.

Hey, don't know if anybody asked about it somewhere else, as I am pretty new to Battlelore (hi all! ), but...
could You please let me know if I can trigger Heroic Necromancers ability called INFLUENCE to move and attack with nearby minion unit while I'm making a counter with the Necromancers?
I mean, it's like I can move and attack in my opponents turn if that's so.

You certainly can. Necros are rather dangerous