verification of wallet to be verified To have btc transferred into a wallet does it need a certain amount of btc in the wallet for it to be verified. Does this amount depend on total btc to be transferred
No,
It is normal to be able to receive money into an empty wallet. Anyone who says otherwise is a thief trying to trick you and steal your money.
Wallets are not verified in any way by the Bitcoin network. Again, anyone who says otherwise is probably a confidence trickster trying to fool you into giving them your money.
Scammers like to use words that have some special meaning in the Bitcoin world and twist them to confuse their victims into doing what the scammer wants. In the Bitcoin world transactions are verified but not wallets. You can use Bitcoin without using any trusted third party such as a bank or exchange. If you do use a Bitcoin exchange they may ask questions as part of the Know-Your-Customer (KYC) laws, but this isn't verification of a wallet.
When you use Bitcoin to pay someone, your wallet creates a proposal for a transaction and sends this to a few other Bitcoin nodes (wallets etc). Those other nodes verify the transaction. The transaction has a transaction-fee included in it but the fee does not depend on the amount of money, only on the complexity of the transaction. The fee is usually very small (cents) but may need to be larger (a few dollars) when the Bitcoin network is very busy.

If you suspect someone might not be being completely honest with you, you can read some answers to questions here that will prepare you for some of the ways in which these kinds of thieves work:

fraud (Bitcoin)
scams (Personal Finance)