Final answer:
The correct way to check all the running processes of a MySQL server is by using the 'SHOW PROCESSLIST' command, which gives details about each process currently running on the server.
Step-by-step explanation:
To check all the running processes of a MySQL server, you would use the command A) "SHOW PROCESSLIST". This command provides a snapshot of the current activities in the server including each running process. It is particularly useful for identifying processes that are not responding or taking too long to execute. Restarting the server or checking the documentation won't give you a list of current processes, and there is no mysql_processes table that stores this information. Thus, the correct answer to the question is A).