Ok I tried my best, but you are simply too stupid to follow basic narrative of this tv series...
He was BLEEDING OUT, his instinct was go to hospital, not lets see if SWAT guys busy with chasing numero uno terrorist should help him, when the only help they can give is drive him to hospital (redundant). And the sole reason Carrie suspected him besides being desperately paranoid is that he was leaving the area, hence suspected driving out Abu Nazir. Well since we KNOW Nazir was hiding in that facility and esccaped the search through that, and not through Galvez driving him away, the notion of him being his accomplice due to that is hence inexistent.
And Saul was overseeing Abu Nazirs burial rites, which btw was islamic, not jewish...(I mean ffs how do you not know this???), and no it wasnt his decision, thats just the basic courtesy Nazir gets, to get a proper muslim burial (even if its thrown into deep sea). And Saul failed the test because it was set up that way, it was a political blackmail by his boss CIA boss, using his shady operations as leverage,similar kind of past most if not all of them CIA operatives have, against him as a way to keep him quiet.