Do Full Nodes validate all transactions and make new blocks after all bitcoin are mined? Do Full Nodes validate all transactions after all bitcoin are mined?
A fork of bitcoin core with all coins pre mined would be behaving in this way too I'd imagine..?
Also, would these nodes still create blocks of transactions, if so, why dont full nodes do this now? Is mining only a safety mechanism for a permissionless network?
See this quote at the link below:

Blockchain Validation vs Blockchain Consensus
It’s important to note that “validation” and “consensus” aren’t the same thing. A Blockchain Validator performs validation by verifying that transactions are legal (not malicious, double spends etc).
However, Consensus involves determining the ordering of events in the blockchain — and coming to agreement on that order.
Essentially, Consensus involves agreeing on the ordering of validated transactions.
The validation precedes the Consensus. We may very well have something that is “valid” that the network does not “agree” upon.

https://medium.com/@BitSongOfficial/blockchain-validation-vs-consensus-4adfce5ac030?_branch_match_id=601696356432534106
Do Full Nodes validate all transactions after all bitcoin are mined?


Yes.


  Also, would these nodes still create blocks of transactions


Yes


  if so, why dont full nodes do this now?


Do what? Validation? If so, full nodes certainly do validate now. In fact, full nodes validating is what keeps miners in check.


  Is mining only a safety mechanism for a permissionless network?


Mining is the mechanism in which the ordering of transactions is determined. It's sole purpose is to dictate which transaction came first in the event of a "double spend" and allow everyone to agree that that transaction was first. It is an integral part of achieving consensus. Mining doesn't actually validate anything; just that whatever goes into a block, and the block itself, must be valid, so miners should be validating incoming transactions before including them in a block.