Is is only Camunda Cloud can use zeebe client and gateway?

If I install Camunda platform with docker, can I control it with Zeebe Client?

This is fixed:

Under the hood, Camunda Cloud is different to Camunda Platform, and this is down to the Zeebe workflow engine that powers Camunda Cloud. The biggest difference is that there is no single database — everything is sharded and replication is between brokers.

also see

Service orchestration in Camunda Platform can be achieved by using its Java API or the [REST API]. Camunda Cloud uses [gRPC].

No, Camunda Cloud (Zeebe) and Camunda Platform are distinct and use different clients.