Building an utxo set and filling your mempool with unconfirmed transactions
=>
Receive a new block, update your utxo db and mempool
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Select the top 1Mb (not countig witness data) transactions from your mempool and create a block. Add the coinbase transaction funding your own address with the current block reward + fees from the selected transactions (fee = sum of the value of all the inputs minus the sum of the value of all the outputs)
=>
create the block header (including the hash of the previous's block header, the root of the merkle tree of all tx's selected in the previous step, the nonce and some extra data)
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Iterate over the nonce untill you find a block header whose sha256d hash is under the current target OR untill a new valid block is received by your node (if you receive a new valid block, go back to the second step of this list)


A secondary loop should continue receiving broadcasted transactions to keep filling your mempool

No.

There isn't any data that specifically represents a single Bitcoin. Rather, transactions references UTXOs (unspent transaction output) within transactions to send the funds. Every transaction, other than the coinbase transaction within a block contains a UTXO to be defined and spent. The UTXO set contains data like the TXID, TX index, block which it's in, script etc, amount, etc.

Bitcoin works like a ledger where the coins are originated from the coinbase transaction in a block but there is no actual representation of individual unique coins.

The ledger should not contain the private keys pairs for each pkh address. Transactions can only be spent by fulfilling the criteria as defined in the UTXO, be it corresponding signatures or specific conditions.

Your previous thread: https://bitcointalk.org/index.php?topic=5304116.0. I didn't receive any response from you but please let me know if you didn't understand any parts of my explanation.

To correct again, the mining software doesn't interfere with the wallet nor 'pays' the miner's rewards. The most it could do is to specify the coinbase transaction and the outputs which are already decided before a valid block is mined.

Mining softwares are usually connected to a pool or node of some sort which will feed it with the information required.

The mining software will obtain the information needed to build a block header from the program. The ASICs merely hashes the block header twice with SHA256 to obtain the block hash. The variables within the block headers are changed with every attempt to ensure that the output is a different hash for every attempt. Only when the hash meets the minimum target, it will submit the correct block header to the mining pool. The mining pool will relay the block across the network and the reward becomes spendable after 120 confirmations.

There's no such thing as a verification node sending coins. Neither will the mining software interact with the coins, it's primary purpose is to supply information to the ASICs. When you're building your block header, you'll assemble a set of transactions and in that set of transactions, there should be a coinbase transaction which would consists of the coins being sent to the address that you've specified.

there is a wrong part at the end about mining software storing coins into miners address after finding the block, this all happens BEFORE the mining even begins because the block has to be created and the coinbase set to send the reward to defined addresses before mining begins.