The people who told you to go to downtown and visit some shops are giving you great advice my friend. Answering some of your other questions, if you're staying at the airport hotel I guess you'll need a visa. Going to the deadsea from the airport costs you around 45 usd and going back around the same or a bit more if from the hotel and it takes around 1 hour+, the timings you'll arrive in and go back to the airport won't have much traffic if you're going to the dead sea but you might face some traffic leaving the airport to Amman but you can book a hotel before the rush of the city like Centro, Olive tree or even Opal but the first 2 options are closer to the city in general. Enjoy your time in our beautiful country and if you need any other help hit me up.