As you know from Ditto's post, you don't need a visa.

Yes, you can interline luggage between RJ & EK without problem.

Rather than paying for a taxi, you can take the Royal Jordanian bus to their city ticket office on the 7th Circle. It only costs JOD 2.

http://www.rj.com/en/to_from_qaia.html

There are great places to eat in Amman, especially Lebanese fare.

If you don't want to spend time in Amman, shell out a few bucks and see the ruins at Jerresh or the old church at Madaba. For that matter, with 16 hours to spare you have enough time to get to Petra and back if you hire a taxi at AMM.

Taxis in Jordan are regulated, not very expensive, run by the meter, and are honest.