So can Verena use a device token from Saska while performing Close Quarter? Both the extra surge and the switching of dice from Power Converter?

I also wonder, Verenas class card "Student of battle" gives you surge = Recover 2. If you dont have any damage can you recover strain instead?

Student of Battle recovers damage only, it cannot be changed to recover strain.

Close Quarter performs an attack, so you can spend a device token in the declare target step of that attack. You can also use Power Converter in the attack provided Verena has not suffered strain upto her endurance.