Is there a way to stick a tag T to a, b and c with one command

You can drag items a,b,c from the list onto tag T in tag selector to apply that tag to all the dragged items.

Is it possible to let a tag be shared by all items of a collection?

You can navigate to a collection then select all (ctrl+A or ⌘+A on Mac) and use drag-and-drop, as described above, to add tags to all items in this collection. However tags are item-specific, not collection-specific, so items added to the collection afterwards will also need to have this tag added manually.

Thank you. Very valuable help.