Hi,
When a user opens a document which requires a digital signature, he/she should see a yellow bar along the top notifying that the document needs to be signed. If the document requires digital signatures from different individuals, and someone has already
signed in, then he/she should see another "MARKED AS FINAL" yellow bar along the top:

Clicking the "View Signatures" button will bring up the "Signatures" pane, there the user should be able to see who already signed.
For your second question, I think it depends on the "Requested signatures" of these documents. If all these documents request the same signature, then the user should be able to use the digital signature to sign all these documents.
Here is the reference you'll need:
https://support.office.com/en-ca/article/Add-or-remove-a-digital-signature-in-Office-files-70d26dc9-be10-46f1-8efa-719c8b3f1a2d
Hope this helps.
Regards,
Ethan Hua
Forum Support