Visa at Jordan-Syria border and itinerary advice

You should be able to get your visa either way. The US passport will likely mean a longer wait at the border than an EU passport, though I'm not sure about Polish passports in particular.

Your schedule looks pretty rushed. Petra is huge and rewards a stay of several days, or two nights anyway. I would suggest Amman can be safely missed. Also you are returning to Damascus a couple of times, when it would seem more logical to go to Palmyra, then to Hama from there, and then back to Damascus.

CK

Agree with the above post. It appears you'll spend time in buses or taxis.

Skip Amman's visit.
Consider a day trip to Jerash from Amman, it's really worth it (great ruins indeed). Easy trip, frequent minibuses and/or taxis. (you can probably also arrange a stop in Jerash on your way from Amman to Damascus)
Dead sea : well... disapointing unless you go to Madaba & Mount Nebo the same day. Nothing to see except beaches and resorts on the shore of weard looking water.You can easily arrange a day tour with a taxi in Amman (just hang out in the area where the taxis to Syria leave)
My recommendation : if you're short of time, go to Jerash and forget the dead sea unless you do want to have that picture of yourself floating in that rather disgusting water (personnal opinion...)

Petra : worth 2 full days. Day 4 is not realistic. The place is not ot be missed.

Day 6 : stay overnight in Palmyra and go to Homs then Krak des Chevaliers from there. Returning to Damascus from Homs on the same day is pretty easy.

Transport is easy to organise.
Amman-Petra : plenty of buses
Amman - Damascus : charter a taxi
Damascus - Palmyra : plenty of direct buses too, takes about 3 hours
Krak des Chevaliers : minibuses or taxis from Homs

Take care

Eric

Hi As Poland is within EU you get visa for Syria normal waiting time half hour. Visa cost around usd 70.If you use USA passport you need to wait few hours.The reward is that you only pay usd 16 for the visa
Post 1 and 2 have good points/comments on your itinerary

Thanks very much for the comments and suggestions. A couple of follow-up questions then:

1) Would it make more sense on Day 2 to hire a taxi and go to Madaba, Mt Nebo, and spend the night by the Dead Sea somewhere (instead of returning to Amman), before continuing on towards Petra the following morning? I've read this might be worthwhile to do the route between Little Petra and Wadi Araba, but would be great to have your take on it.

2) If you suggest skipping Amman altogether, is it feasible to get from Petra to Damascus then directly on Day 5? About how much would this cost?

Cheers again.

NO there is no direct public transport from Petra to Damascus.There is bus JETT leaves 4 pm arrives amman near Abdali Garage. 7 pm.Take a service taxi from Abdali to Damascus you arrive by 10-11 pm to your Damascus hotel.