Yes, this process will run only the selected trigger.
However, it will if the trigger you are running is internally invoking any other trigger.
Yes. It runs only selected trigger. It would not run other triggers.
Yes Wim your assumption is absolutely correct.
Trigger used to update field --> Field Updated --> related trigger run because the field is updated - This is how it will and should be working.
This option to select/not select triggers is an just an option/utility to ease when someone want's to run multiple triggers at a time instead of running one at a time.
Do you have any specific reason or test case on why you don't want to run related triggers?