Hi Nermin, and welcome to the community.
I'm afraid I only have half an answer:
1) What is "split on module"?
2) Have a look at the "created vs resolved" gadget. This is exactly what it is for!
I assume you are setting the departments with a field like components or a custom field to put it on each issue.
Two steps to this - first, run a filter for the issues you want to see ( "created > -1w" for example) and save it.
Second, use that filter in a dashboard gadget. The most simple one is probably "filter statistics", with the "statistic" set to look at the field you are using for "department"
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