How is Intl to domestic connection at the new airport? Is it like old IST where you need to clear customs then walk from intl arrivals to domestic departures? Or can you go to domestic terminal after customs without clearing security again? Also is it separate entrance again for J passengers with a bus from the lounge to the gate?
I have not flown TK business recently - TK has been way too expensive vis-a-vis other carriers of the same or better quality on routes to both Asia and North America - but I can share my economy class (i.e. no frills) international-to-domestic and vice versa transfer experience (flying from Europe via Istanbul to Izmir and back).
i) Plane taxing times after landing / before take off are insane, I suggest adding up at least 1 hour on the top of your minimum required / recommended connecting time to make sure you do not miss your connection. Landing after my first flight, it took us around 35 min to reach the gate (around midnight), on flying out of the domestic gates we taxied around 25 min (with almost no traffic at 2am), on flying in from Izmir we taxied again around 25 min to a remote stand (around 2pm), and finally when flying out from the international gates we needed another 30 min before taking off (around 5pm with only a few planes in front of us in the queue).
ii) The terminal is massively big so be prepared for a lot of walking. My incoming international flight docked at gate A11 and my outgoing domestic one was from gate G7 - this required a good 1 hour of walking. On the way back, we were "lucky" to be bussed to the center of the terminal and from there I needed "only" 20 min to reach gate B12 for my international flight. There are apparently buggies that can drive you around - at the price of €16, if I understood well.
iii) Under normal circumstances, you will not have to clear customs in Istanbul. There is a very detailed explanation on the website of TK but in essence as long as your destination domestic airport has customs control (which should be the case in the majority of the cases, but a full list is available on the TK website as well), you clear customs there - what they do is split the luggage of the passengers, whereby the luggage of purely domestic passengers is routed to domestic arrivals while the luggage of international transfer passengers is routed to international arrivals. On the way back, you obviously do not need to go through customs in Istanbul if your luggage is checked through to your final destination.
iv) Nevertheless, both ways you will have to clear first passport control and then security (non-event for me as the wait was no more than 5 minutes in all occasions).
I hope this covers what you were looking to understand - any other questions, feel free to ask.