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The Carnot cycle is an idealization of the Carnot process. It is not a practically reversible process due to the fact that no engine can be% efficient. Carnot cycle requires an engine or a process to be both isothermal and adiabatic in nature. An isothermal process would need a zero thermal gradient condition to transfer heat which is not possible in reality.
The carnot cycle is only used as a perfect upper limit for designing engines etc... in other words, used as a reference point. The actual condition will be a percentage of this upper limit. This is called the carnot efficiency.
Yes, Carnot cycle is a practical reversible process in thermodynamics. Carnot heat engine operates on that cycle.
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