Does it x-reference which transactions were included in the loosing but not he winning fork?
No. Orphaned blocks and their transactions are not stored and referenced. Some blockchain explorers may store the orphaned blocks that they received in their database for public viewing, but that's unrelated to how the Bitcoin protocol works.
What happens after chain reorg with the transactions confirmed on the shorter chain (lets assume a somewhat possible 3 blocks reorg), but not included in the longer chain? I believe those are not in the mempool anymore as they were included in a block earlier.
Does Bitcoin core re-queues the transactions from the overwritten blocks?
"The" mempool does not exist. Every node has their own mempool. That means while nodes that followed the "losing" fork will have removed the transaction from their mempool, other nodes that have been following the "winning" fork all along will still have the transactions in
their mempool -- given, of course, the transactions have not yet been included in the "winning" chain as well.