Does Polystyrene contain benzene rings

Yes (and no!)

The styrene molecule is a benzene ring with a -CH=CH2 group attached. In the polymerisation process, the double bonds in two adjacent groups are broken and joined to form a chain:

-CH-CH2-CH-CH2-CH-CH2-CH-CH2-....... with a benzene ring off each -CH- group.

I believe the benzene group is referred to as a "phenyl group" in complex molecules, such as polymers like polystyrene.