Can I make rewards available only to certain customers?

Yes. You can make rewards available to a specific customer group = segment. To do this, create a segment and select it as a prerequisite in the reward settings.
We distinguish between two view options here:
-All contacts see this reward, but can only redeem it if they are assigned to the segment.
-Only contacts assigned to the segment see this special reward. 

You can find out how to create segments HERE. 

You can find everything you need to know about adjusting your premium HERE.