TK will check your baggage to your final destination in the US when you show your US-itenerary to the agent in IST.
2.5 hours in March should be fine in MUC. Winter is - hopefully - over and now snow.
You have to clear immigration in MUC which is fast and efficient. TK and US are in the same terminal so you just have to go to the main hall, find the US counters and check in for your onward flight.