For the heat engine:
First I converted all the temperatures to Kelvin,
ηmax=1-(333)/(1000)=0.667
ηclaim=(1*10^3)/(1.75*10^3)=0.5714
So the heat engine seems to be less efficient than a Carnot heat engine which means it can exist.
For the refrigerator:
COPmax=(253)/(363-253)=2.3...