STDs testing

I would imagine that pretty much most of the hospitals would have those tests.

However, I wouldn't recommend doing HIV and Hep tests in any GCC country if you suspect that you are positive (have any symptoms) as pretty much all countries have strict reporting guidelines to the Ministry of Health on these type of diseases (no patient confidentiality on these diseases by law) - which can lead you to being deported.  What is reported varies from country to country i.e. they may report stuff like Syphilis even.

The closest you can get to anonymous testing in this part of the world is in Dubai.  Check the UAE forums and search for Zack Medical center - we had a big discussion on that recently.