How to know the number of emails to a specific support email address?

You can route emails sent to a specific support email address to a group directly from Admin--> Email. 

However, if you have the tickets being shuffled between groups on a regular basis, you can make use of the Dispatch'r to add a tag using which you can filter the tickets. 

Navigate to Admin--> Dispatch'r--> Create new rule. 

Condition:

"To Email" "is" "The support email address"

Action:

"Add Tag"