Transaction Priority and Finality

Is it possible to prioritize transactions by paying a higher fee?

The current official software does not prioritize transactions based on fee.
As long as the transaction’s fee is sufficient with regards to minimum fee (and congestion rules if there is congestion), the transactions are added first come first serve (from the point of view of the block proposer - note that all nodes may not see the same order).

In theory, participating nodes can run modified Algorand software that would prioritize transactions differently, but my guess is that currently it is not the case.
That does not mean that it will never be the case though and the above property cannot be relied upon for any security-related concern.

The title also mentions “finality”. As soon as a transaction is added to a block and the block is added to the blockchain, the transaction is final. There is no possibility of re-ordering/re-organizing transactions, adding transactions before, or forking in any way.