Hi @Hiep_Tran,
Welcome to the community
Just to add to @Skyge's excellent answers (thanks as always @Skyge )
I recommend reading how USDC did their upgrade: https://blog.coinbase.com/usdc-v2-upgrading-a-multi-billion-dollar-erc-20-token-b57cd9437096
Also the current state of upgrades
Yes there is a gas fee overhead using a proxy. I recommend testing this yourself on a public testnet to see the difference.
Please note this condition: OpenZeppelin upgradeable contracts affected by Istanbul hardfork
The proxy and the ProxyAdmin contracts should be already verified, your implementation contract won't be verified.
Etherscan supports proxy contracts.
I wasn't sure what you meant?
Aside from a gas overhead, you have an administrator account that you need to keep secure and your community need to trust the management of.
See: https://docs.openzeppelin.com/learn/preparing-for-mainnet#set-admin
You may want to use a multi-sig such as Gnosis Safe and use OpenZeppelin Defender to administer (see: https://docs.openzeppelin.com/defender/admin).