If you want to transfer your money from a US bank to a Turkish bank and if you will have to pay a transfer fee depends. My bank in the USA does not charge a transfer fee as long as they are sending it in local currency(Turkish liara), but if for example you have a US dollar account in Turkey then they will charge a 40 USD international wire transfer fee.
It is better to keep your money in USD or in the USA and then to send over the money that you need each month. There is western union, money gram, and many other money transfer services in Turkey. Currently the Turkish Liara is not stable, and it is better not to keep your currency in it since you never know if it will go up or down.
To start a bank account you will need to apply for your temporary residence permit, then register with the population office, and then go to a bank that is willing to do business with Americans.
You will find many banks in Turkey even though they claim to speak English do not. So it may be best to hire a translator to go with you. Also many employees at the banks don't even know their own rules when dealing with international customers, or have never bothered to even read them. So you will have some bank employees tell you its not allowed to deal with international clients even though this is not the case. You will have to really look around. The only bank I was able to start a bank account with, and have no problems with was Isbank.
You will also find the same thing when dealing with trying to get your internet, your phone, dealing with utility bills, etc.
When I went to the stores to try to get my internet set up I was told multiple times that you couldn't get internet if you werent a turkish citizen, or have any utilites like gas or eletricty if you where not a turkish citizen.
I had others tell me that my ikhmet card had to be from their specific city, and had everyone down the line tell me all types of wrong things.
The only way I was able to resolve this all was calling the English helplines that the companies set up, and talking with the representatives directly which where super helpful, and even told me that none of these people know what they where even talking about. Even some of the customer reprenstives admitted that the employees where lieing, and just didn't want to deal with foreigners.
You will find Turkey to be a xenophobic country, and even as an American I have had troubles here. If you have anymore questions the feel free to ask me.
You will also run into the problem of renting an apartment here if you don't want to buy an apartment or house because 80-90% of the turks will not rent to foreigners at all.
Even though we could be sued in the USA if we ever put into an ad "No foreigners allowed" it is very common to see in Turkish ads where they will put on their apartments or houses for rent "No foreigners allowed" and as far as I know there is no rules against it because they keep doing it.