Hi there!
I hope you are doing fine.
The questions you have put are from thermodynamics and I already have an idea of how to go about it. Just a little bit of calculations are required for each question.
Also you need to provide the diagram given in your class for Atkinson cycle.
However, considering the usual Atkinson cycle diagram, I shall provide you answer for Q. 2 right here.
Q.2 a. There is no work associated with 5-6 because during 5-6 heat is rejected to surroundings at constant volume. Since the volume is remaining constant there is no work. In reality, during 5-6 exhaust valves are open and hot gases simply escape to atmosphere.
Q.2 b. Process 4-5 is assumed to be an Adiabatic process and during adiabatic process there is no heat exchange with the surroundings. In reality, there is very little heat lost to surroundings because the process 4-5 is very fast and very little time is available for heat exchange.
I hope to answer rest of your questions.
regards