Hey Maverick,
There is no computation in the beacon chain so gas is not needed there. The shards will have an execution engine so they will use gas for executing transactions. So ether will be used for gas in the shards.
Validators will be rewarded mainly through new issuance of ether but this will be far less relative to what miners currently get. So the inflation rate of ether will be reduced considerably. They will also be rewarded by transactions fees etc.
The new network will be secured via the encompassing Proof-of-Stake system. Validators will be incentivised to act appropriately and report those that are not acting appropriately.
The difference is that the system as a whole can support far more transaction throughput which would make it more usable for more use cases than it can currently handle today. So basically any use case that smart people think of in the future.
