Sending directly from mobility

Can you send images directly from mobility? Can you set up a DICOM storage server that listens for dicom files on network?

I don’t understand the first part of your question. What is “mobility”?

Regarding the second part of your question, Orthanc is precisely a “DICOM storage server that listens for dicom files on network”:
https://book.orthanc-server.com/dicom-guide.html#dicom-network-protocol