Is it possible to execute a query and receive a result in the API, the same as the queries tab in Impala?
Cloudera Manager does not have an API entry point to allow you to execute queries. You can view queries and cancel them, but CM will not execute the queries.
For a UI to do so, you can leverage Hue.
The exhaustive list of all Cloudera Manager API commands is available in it's documentation. As Cloudera Manager API is designed to manage and provide information about the cluster status, it has currently no capabilities to research the data itself, like receiving the result data of Impala queries.
I'd recommend to use impala-shell or one of the available connectors (ODBC / JDBC) to interface with impala, depending on your specific use-case.