Why does Carnot Engine have the curves as isothermal and adiabatic?
By definition, a Carnot cycle is comprised of 2 reversible isotherms and 2 reversible adiabats.

Regarding your question about isochoric heating or cooling, if you are going to carry this out reversibly, then you can't do it with just one constant temperature reservoir.  For the heating or cooling to be reversible, the temperature difference between the system and the reservoir(s) must be tiny over the entire path.  To do this, you need a sequence of constant temperature reservoirs running from the starting temperature to the ending temperature.  After the system has equilibrated with each reservoir in the sequence, you move on to the next reservoir.  That way, the temperature difference between the system and the reservoir is tiny along each step of the process path.