Hi Efrem and welcome to Jordan!

Lack of Arabic should not pose any problems....I mean not all of us can write essays in english,but there should be no problems with understanding.

Driving takes around 3:30 if you are not speeding too much,buses -4:00-4:15. The disadvantage of the bus is that you may get unlucky and spend a long time at Customs check point (Aqaba is a Special Economic Zone,hence the customs check point).

This is the website for the bus operator:http://jett.com.jo . If you do end up taking the bus,then I would highly recomend the VIP bus option from 7th circle. The added comfort is well worth the premium. The website has all the prices and the timetable.

Not sure why you want to rule out flying? You can take the morning (RJ 300) flight and still be well in time for breakfast in Aqaba and then cross to Eilat? I wrote extensively about AMM>AQJ flights here,so you may want to check it out

RJ domestic flights guide (including connections/AQJ airport transportation)