If a transaction happens and it verified on a blockchain and the miner receives Bitcoin for the proof of work does is the Bitcoin miner received count as another transaction that then itself has to verified and add to ledger Or the transactions only verified and added to the ledger occured when Bitcoin is sent between and individuals rather than earned through mining?
About miners receiving coins:
First of all, the miners in the way blockchain sees them are the solo miners and the pools. They don't receive reward for blocks they mine (see it as a competition), not just because they're working.
A mining pool that managed to mine a block (i.e. add it to the ledger/blockchain) will receive the block reward and the transaction fees of the included transactions and all this is part of the coinbase transaction. (Here) it's not a separate transaction.
The miners from the pool will get then coins based on the pool calculation and based on the amount of work they've done. The miners will - sooner or later - withdraw their earnings, clearly, as different transactions.
But, coming back to the coinbase transaction, there is no separate transaction for paying the transaction fees, neither between the blockchain and the mining pool (the transaction fees are delivered in the same "special transaction" the block reward is also delivered - actually better wording would be
claimed), nor between transaction sender and the mining pool.
About transaction verification:
A transaction, when it's sent, all the inter-connected nodes will verify it when they receive it. Ultimately, the miner node, depending on the fee used by the transaction, how busy the network is and other rules, will include the transaction into a block when it will mine it (keep in mind that blocks are mined at an average of 6/hour).
When one sends transaction to another, the recipient will probably see it almost instantly, but that's an
unconfirmed transaction which is safe to not take into consideration until it actually gets confirmations (without confirmations you can see it only as a promise - which can sometimes be an empty promise).