There is a thread about *A awards here: Everything You need to know about booking Star Alliance awards with Miles&Smiles

For your question, unless there is X fare bucket availability for Economy and I fare bucket availability for Business Class, TK would be unable to rebook you on another United flight.
Unless your flight is within the next 15 days, TK would not rebook you on a flight without award availability, however, you could still take your original fights unless you cancelled them.

In addition, calling UA would also not be useful as they would refuse to touch a booking issued by a third-party agent which in this case is Turkish Airlines.