Best time to check for open seats online (or on phone) is EXACTLY 23 hours and 59 minutes before the flight leaves. I mean exactly.

Regarding the handicap, you should have a written doctors note (not just a "he said"), but a actual written prescription to present to the GA. This is often called a "FIT TO FLY DOCTOR'S LETTER". It should be clear as to what the handicap is and what is required medicalwise. As previously stated, this will negate any possibility of exit row. They do have handicap seating in certain rows reserved, but I've found its mostly up to the GA's to assign them at the last minute.