Did I choose a fake bank?

When you are asked for codes that cost money, you know the goal of the transactions to to scam real money from you.

The bank isn't real. The cheque isn't real. They person isn't who they said they are. The reason why they sent the cheque to you and that you needed to use a specific bank was designed to get you to start the chain of transactions.

Sometimes they send you a fake or stolen cheque and allow you to deposit the cheque into any bank. In that case the goal is to get you to pull real cash from your bank to send to somebody else, before your bank realizes the cheque bounced. In that scam there are no expensive codes to slow down the money transfer.

If you check on Google, a search for "turkvana" will show nothing except their own website, turkvanabank.com. I would conclude that the bank doesn't exist, and that it is a scam from start to end.

No real bank ever asks you for money. They will take fees out of your account, but they don't ask you for money. That's a very good way to identify scammers. This works in other situations: No lottery will ever ask you for money to get your winnings. If there are fees, then they just pay out your winnings minus fees. An employer will never charge you for a job. If they have fees to pay, they take that out of your first paycheck.