Usually you will be able to do OLCI. If not, you just go the TK transfer desks to check-in. You def. do not need to go through immigration and enter Turkey.

We have yet to hear any reports in this forum that dupe bookings (on different flights) are a problem with TK. Most likely you will be fine.

Assuming that your flight is o/w JFK-IST-KTM there is absolutely no issue with skipping the last leg.