There are about two dozen regional/commuter rail systems in the U.S. that are not operated by Amtrak, but also would never be confused with urban rapid transit systems. They are not designed for long distance travel by tourists, but a backpacker could make the journey from New London CT all the way down to Newark DE (about 250 miles) entirely on commuter train services for about $50 (plus a walk between Grand Central Station and Penn Station in New York), as opposed to $127 on Amtrak.
In some cases they share facilities or lease rail from Amtrak, but to the consumer they have no other relationship— you can't go to a Metra agent and ask whether the Empire Builder is departing on time, and you can't go to an Amtrak agent at Washington Union Station and get a VRE pass. So while we wouldn't need a tag for each of those systems, it wouldn't be correct to tag them as Amtrak, either.
No - see @choster's answer. (The tag is presently in use for 43 Open questions.)
use the most specific tags for the question.
Technically Yes, but very far from being practical or ever being implemented.
But I agree, it seems weird to have all these, it looks like too many.
Are synonyms one-way or bidirectional? In other words, is there technically a way to "produce" the tags trains and united-states when amtrak is used, but not the other way around? If so, I would suggest this. If not, let's just tag the three.