Sometimes;) If Picard was able to find an AcoustId, yes you should see such a tag for the file. If not, then not. But you can do a “Submit” (after matching the file to a recording) and a “Scan” again and you should see one.
Yes. It kinda does, but it is not very visible. The messages show up in the status bar at the bottom, but are quickly overridden. You can see them all in Help → View Activity History. That’s maybe the most fundamental flaw in the UI that it is often not clear what is happening.
You should see something like this in the output:
10:41:33 Looking up the fingerprint for file '/home/phw/file1.mp3' ...
10:41:33 No matching tracks for file '/home/phw/file1.mp3'
10:42:08 Looking up the fingerprint for file '/home/phw/file2.mp3' ...
10:42:08 File '/home/phw/file2.mp3' identified!
10:45:00 Loading album 923a1458-ffc0-425c-93fe-73404eecbedf ...