First off I want to say thank you for sharing. That takes courage. Second, the Disclaimer: NOT A DOCTOR or otherwise intelligent person. This following is my opinion only does not constitute medical advice or relevant information for your particular situation and is provided for entertainment value only.
As to what happened? Hard to say. Could be many things including but not limited to:
1. An undiagnosed condition that has developed recently (potential result of recent lack of exercise and increased weight)?
2. Too much party the night before. Alcohol within 24 hours of diving is not a great idea. It dehydrates you and that increases your risk for DCI.
3. No enough water the day of and the day before
4. Physical conditioning. Being out of shape and having to fight the currents.
5. Exercised induced asthma or other lung issue.
6. Hyperventilation - easy to do. You are in an overhead environment 20 feet long (why do dive operators insist on calling these overhead environments "swim thru's"? ) and fighting current. Easy to start over breathing the regulator, panting and causing hyperventilation. This is the result of CO buildup in the lungs. CO is what triggers the body to take the next breath. With this shallow panting type of breathing you are not getting the CO out and Oxygen in as you are breathing shallow and fast. (When this happens, hug yourself, tell yourself to calm down and take slow deep breaths. S L O W Inhale 1,2,3,4,5,6, S L O W exhale 1,2,3,4,5,6,7,8. A few breaths like that will relieve the "can't breathe" feeling and of course the resulting headache will clear up shortly too.
7. fatigue - you were fighting current and surge. SURGE - you can't fight the ocean, just go with the flow. the surge will bring you back and you just have to get a quick glance as you pass it. Fin slowly when the surge is going the wrong way and hard when the surge is going the direction you want to go. Current - swim into it at the start of the dive. When you failed to be able to grab the dead corral and to get back to the reef, you were going to be blown away from the boat. Chill, nothing you can do about that. Ascend in a controlled manner while swimming into the current (but don't exhaust yourself). On the surface inflate your BCD (you dropping your weights and not inflating BCD is an indicator that at this point you were in full panic mode) (Congratulations by the way on dropping the weights. Good call when you are in distress).
8. **** happens.
Any one of the above could account for the situation, but very likely it was several of the above or maybe something else entirely. We often talk that accidents are never one thing, but often three things. Example, out of shape, partying hard, drinking, limited surge experience, unexpected current, 20 foot overhead environment, nervous.
Now to your questions.
What I do not understand are the following factors I did not have control over, and am asking for thoughts on, are the following questions: (My answers are in brick red. OP questions in black) I don't necessarily agree that you did not have control over all of the below. You picked the dive operation, you got on the boat, you left the dock. Did you check to see if they had O2 on board and how big the tank was and if it was full? How about an AED? Did you inquire about the emergency procedures if you drifted away from the boat? Did you chat up the DM and ascertain if they were certified DM by an accredited agency or just SCUBA divers with out without formal training in how to dive? Who is responsible for checking these things out? Answer, you are. Its your life and your dive.
1. How did I end up out there alone, when the Master in training was bringing up the rear?; As already stated, you were never alone, just separated. Others found you in seas that were rolling a bit, so they must have been close. They also did a controlled ascent, and by your account, you did not.
2. Why did that non-diving Dive Master wait 12 minutes to swim out to us when it was clear, even to 2 non-swimmers, we were drifting AWAY from the boat? A couple of questions here: A.) Was the Non-Diving DM also the only crew member left on the boat? B.) Did you have assistance immediately at hand in the form of a certified diver and then a DM? (yes you did). Were you out of range of the current line the Dive Boat had? If so, then would you rather add another to the crowd drifting away or wait for the DM to recover the other divers and bring the boat over? C.) If the group you had with you could not swim back to the boat then what makes you thing the DM on the boat could bring you back to the boat? Inflate the BCD, sit back and relax. Focus on the S-L-O-W breathing. D.) Did you give the DM the one arm up not moving signal (need assistance, but not emergency) or the two arm waving (or one arm waving) signal of HELP, come quick. (remember the boat can't move with divers in the water for fear of running them over, and you already had a DM with you.
3. Why was the emergency O2 so difficult to access, then correctly administer (the hole where the air flows from should be under your no, not askew on your cheek.)? In non-Sue-Happy USA countries, you will sometimes (often?) find dive operators that ....um, well, don't pay close attention to standards. Was the DM a certified DM or just a diver they hired to be the DM? The DM's and boat crew all should be O2 Qualified and familiar with the equipment. No excuse here. It is their boat, their crew, their DM and their O2 kit, they should know how to use it. In non-sue happy US some dive operators take a more laid back approach to diving and diver safety.
4. Is emergency O2 supposed to "run out" in 10 minutes? O2 tanks come in different sizes just like SCUBA tanks do. Small ones last ~12 minutes or so, bigger ones longer. They are not cheap either. www.diversalertnetwork.org/dive-store/?catNo=9 shows the price. ~20 minute supply $475-$625, ~60 minute kits, $650-$800, ~120 minute kits, $750-$899. ideally the dive boat should have a tank large enough to get you from dive site to shore. Getting the inspected and hydro tested every 5 years and then filled again. Medical grade O2 is not cheap and in some locals around the world not that easy to get either. Where you were, it sound like a good bet the nearest place selling medical grade O2 was not within 100 miles.
5. Do Dive Masters get any training regarding the effects of exhaust fumes on an already distressed diver? Yes they do. But in the heat of the moment it is easy to get tunnel vision and be focused on getting you out of your gear, back on the boat and breathing again.
6. Why didn't the boat have portable O2 bottles? Like a couple of ponies? I went an extra 8-10 minutes on that golf cart without O2, there are no ambulances on Harbor Island, so anyone having O2 problems has to be transported somewhere. A pony would have helped a bunch on the golf cart ride to the clinic? Their O2 bottle was most likely portable, just empty. If they had had a portable O2 bottle, they would have given it to you when the first supply ran out.
Again, glad you survived and hope you will make a full recovery and tanks for sharing.