How can I assign a shared label to a document?

If you have the role of a "Sender", when creating a document you'll be able to use an additional "Document labels" field and select the labels to which you want to assign a given document.

Why can't I tag a document with a shared label?

It seems you don't have a "Sender" role in the shared labels. Contact the label owner to grant you this permission.

Can I assign a label after sending the document?

You can assign a shared label only when sending the document. You can't add a label after you've already sent the document.

Can one document be assigned to more than one shared label?

Yes, you can assign a document to more than one label.