For context, a group of characters are on a quest to recover a religious artifact stolen from Jerusalem by the Sassanids and they figure their best bet is to go from the port of Kazma (modern day Kuwait) to the Persian capital of Ctesiphon? I know the Persians were famous for their road networks, but I want to give the travel a better description than 'these characters went from Kazma to Ctesiphon'. What kind of obstacles and hurdles would they have to go through to reach the Persian capital?
i'd look at terrain maps. also, if its a main road, there were probably bandits. wild animals, too. look at Ethnic makeup as well, because perhaps there were conflicts between the different ethnic/cultural/religious mixing of people that could contribute the the hurdles these characters face. Were these roads taxed? perhaps they didnt have the tax to use the roads and have to go off into the wild
It sounds like it was a pretty well-connected trade stop. I don't know the topography but maybe someone would sail north into the Meshan district and then from there they could follow the Tigris to Ctesiphon. Assuming the relics are Christian (I'm guessing the ongoing Roman-Sassanid beef has something to do with the theft?) there would be Christian communities along the way and probably some sympathetic contacts.
Are they traveling by road or by sea? You did mention a port. If it's by land, the roads might be hazardous, depending on how well kept-up they were, and what season it was. There could be massive potholes or ruts that become like little gullies. Thick roots growing up through the ground, big rocks etc. Maybe wild animals. Would these be dirt roads, or paved somehow? Keep in mind, what was considered magnificent roads back then would be like our alleys or back roads at times, just as the greatest kings and emporers didn't have hot and cold running water or air conditioning and central heat. Some of the poorest among us today live in luxury kings could scarcely imagine then.
When exactly in the 7th century? Ctesiphon fell in 637 and the Sassanids were pretty much constantly at war until then. After that date, the city was no longer under the control of the Persians, and the Sassanids had fallen, to be replaced by Muslims.
Your talking about desert travel, here. Which would be traveling from water source to water source. Any delay, could prevent the group from making it to the next water source.
Most of the journey would be probably be up or along the Tigris so not really that kind of desert travel. You would find arid places but also farmland and marshes, maybe some forest even.
It's not even particularly desert. That area is part of the Fertile Crescent, and has been since Biblical times.