Is blockchain statry and UTXO apply?

As long as I understand, I download more than 500 GB blockchain data to be used to check the combination of blockchain when the new node joins the network.

It is difficult to rewrite the blockchain, but it is easy to check, so start with the header check from Genesis Block to Tip Block to check whether the downloaded blockchain is damaged.

Then, the text of the block is repeated from the Genesis block to the tip block, which takes a few days or weeks to configure the UTXO (current balance of each address).

About all blocks while repeating:

• If you are output from the transaction, add the address to the UTXO set.
• If you are input (source) in the transaction, remove the address from the UTXO set.

Therefore, the blockchain itself is to store the transaction record because the append operation allows to create a new block.

In this stateless data, all nodes can configure a state of UTXO set if all nodes maintain their status in the internal memory (like the remembers stored). correct?

In exactly, the average UTXO of all nodes may be different.

Please clarify my understanding.