I'm a bit surprised by the lack of understanding of basic Bitcoin principles, to be honest. There's a cure for that: e.g.
https://learnmeabitcoin.comEvery time we initiate transactions, miners validate those transactions and ensure no double-spending occurs.
No, not only miner's nodes validate new transactions but every Bitcoin node does this when they get a new transaction relayed to them by their peers, because every invalid transaction has to be dropped by honest nodes and is not allowed to be relayed.
A Bitcoin node has no reason whatsoever to trust any of its peers to play fair. Your or a miner's node doesn't have to trust other nodes, it can and has to verify if a new transaction is valid or not. Trustless decentralization mandates that a node verifies itself if things are valid and drops everything that isn't. Malicious nodes that relay invalid stuff are isolated and ignored by honest nodes.
You can argue that miner's nodes have a particularly strong incentive to deal only with valid transactions because any invalid transaction put into a newly mined block would make that block invalid and dropped by any other node in the whole network. Mining an invalid block is wasted time, energy, money and lost rewards.
Recent published invalid blocks that my node saw e.g. were at blockheight 783426, 784121 and 809478. Big software fails of the involved mining pools. (There was some discussion about it at Bitcointalk because it was an expensive oopsie of the responsible pools.)
The transactions fees we are charged goes to the miners. Our only concern should be that when all the bitcoins are mined and miners no longer get rewards, they might likely shift their attention to transactions fees and charge higher fees. We really shouldn't bother about this because we might not witness this period when there will no longer be bitcoins to mine.
You slightly contradict yourself. How can you say "miners no longer get rewards" when they always can collect all transaction fees of all transactions of a mined block?
I repeat again, as long as the Bitcoin blockchain gets extended with new blocks there will be bitcoins to be mined (at least from transaction fees). Don't forget: every UTXO traces back to newly generated bitcoins from a coinbase transaction. This doesn't change when the block subsidy has dropped to zero and only transaction fees are mined to "fresh" coins
of infrom a coinbase transaction of new blocks.
I don't see much of a reason to not call miners miners even 125+ years from now. They still will have to grind blockheader hashes to find a valid one to extend the blockchain with a new block.