I will be moving from the USA to Riyadh, what is monthly rent and any leads for places with a roommate?
I'm actually an Expat Arrivals employee - I haven't actually been to Riyadh myself - sorry about that! But from what I hear the Western compounds there are really nice and there are generally fewer restrictions within the compounds than outside as the Saudi Arabian religious police don't tend to involve themselves there. I mentioned the Accommodation in Riyadh page before - there's a section there about compounds in particular.
All the best with your move.
The Expat Arrivals Cost of Living in Saudi Arabia page has information that should give you an idea on how much to budget on rent each month. See the cost of living table at the bottom of the page in particular. You also may find the Accommodation in Riyadh page to be of use, too, just for general info.
To find a roommate you might try advertising online or advertising on local notice boards once you are in the area (to do this you'd need to stay in short term accommodation at first). Be sure to meet any potential roommate in person before agreeing to live with them.
Best of luck
As long as your phone is a GSM capable phone (as opposed to CDMA), you should be able to use it in Saudi Arabia, though many phones are locked to a particular network so you may have to get your phone unlocked before a local SIM card will work. If your phone uses a SIM card, it is a GSM phone). More info on staying in touch in Saudi Arabia here.
Some medicines are restricted in Saudi Arabia - you can find a lsit of UAE restricted medicines here. There doesn't appear to be a specific Saudi list online.
These medications may be more difficult to find at regular pharmacies and if bringing them into the country, you will need to carry a prescription and/or doctor's note with you as proof you've obtained them legally. To be safe you can also try to get this document certified by the Saudi embassy in DC.
Make sure you know the generic name, formula name, and common brand names of the medication as the exact names can differ from country to country. I suggest googling these with the term "Saudi Arabia" and seeing what comes up.