Is newton's third law valid in non-inertial frames? For example, in a rotating frame of reference, can Newton's third law still be applied? Or does the non-inertial character of the frame violate it?
Only if the second law is not valid. But usually the second law is assumed to be valid in non-inertial frames. This results in pseudo forces violating the third law.
Welcome to PF! Hi Debdutta! Welcome to PF! As between two objects in contact? Yes, the forces will still be equal and opposite.
The forces acting between two objects do not depend on the coordinate system or referemce frame you use to measure them. So the third law always holds. The second law is different: the apparent accelerations that you measure DO depend on the reference frame, hence the second law does not hold in a accelerating frame unless you add another term to the equation (a.k.a a fictitious force) to compensate for the acceleration of the frame.
So my next question is, can we assume that Newton's Third Law is still valid for interacting objects in any frame to test whether it is actually an inertial frame or not, that is, the first two laws of Newton hold or not?
Yes. You can always assume that the interaction forces between objects obey Newton's Third Law. If the sum of all interaction forces on an object and its coordinate acceleration are not consistent with Newtons Second Law, then you know that your frame is not inertial.