BPMN - possible but not necessarily arriving tasks- Which Gateway
Which gateway should I use to describe a possibly, but not necessarily arriving task?
The following screenshot demonstrates the situation: 
Which gateway can explain after the main department did the Task A, that
everyone (Supporter 1, Supporter 2, and Supporter 3) can help, but does not have to?
Is the exclusive gateway the correct one?
The type of a gateway you're looking for is Inclusive Gateway. As described in BPMN Poster
Inclusive Gateway
When splitting, one or more branches are activated. All active incoming branches must complete before merging.
Note also that the message receiving intermediate gateway is used to show communication with other pools, but not inside one pool.
I would also recommend using merging gateway, especially when using the gateway with such specific behaviour.
Your diagram could look like this
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