I see extra ArcSOC.exe processes and some are even visible after I stop all my services

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ArcGIS Server uses two ArcSOC.exe processes internally for logging and directory management. You will still be able to see these processes running in Windows Task Manager even if you stop all of your services in Manager or ArcCatalog.

Additionally, geoprocessing services use multiple ArcSOC.exe processes to manage scheduling and status of jobs. For each geoprocessing service configuration, you will see one ArcSOC.exe process, plus two ArcSOC.exe processes for each running instance. For example, if you have one geoprocessing service with three running instances, you will see seven ArcSOC.exe processes. These processes will go away when you stop the service or shortly thereafter.