If your health is low and Sydney is breathing like she is tired, get away from all targets and wait for awhile. Her health meter will go back up. Note: This may take awhile.
On the Asylum mission, there is an elevator. The code for the elevator is "4747". You can get the code by talking to Neil Caplain, who is located in one of the padded cells.
When you are trying to get the man's DNA and must follow him, once you get in the room with all the picnic tables go to the right side of the door and stand there. He will walk by time after time until you get all of his DNA. You will then fight him, escape from the Asylum, then move on to the Embassy level.
When at the end and you have to turn on all the fire alarms, one of them is in Basement 2. Note: After you turn on all the alarms you must hurry to the ballroom and fight three men, then find Dixon and escape.