Is there a good reference on being able to sip a little air from an empty tank as you surface. I keep seeing and hearing references that a tank will expand as you surface allowing you to get the extra air. It was referenced earlier that your regulator will adjust to the pressure change giving you the extra air which I understand.
You got the first part corrected by the above hopefully perfectly clear post by radtype.
For the second part, the reg will most definitely not make it easier to get the last breath out of a tank. It is (usually) very much like sucking marbles through a straw to get the last bit of air for most regs, because there is very very little excess pressure over ambient in the hose running from the first stage to the second stage.
By comparison, hose runnning to the second stage usually has something like 10 times the ambient pressure running to it. (That's a vast simplification, the sort of vast simplification, that as a divemaster, you should really think about not having to need, but ...)
This is not how gear is designed to be used, and you can flood a first stage, and a tank easily doing this stuff, requiring overhauls etc. etc.
There are some distinctions at play here:
1. Divers: I think
recreational divers should be comfortable handling CESAs from whatever depth they dive to. Easy and safe enough to practice with a
full tank and all gear in place. Divers should always maintain there gear in place, and should never intentionally ask for trouble by running tanks to empty, etc. If a diver questions whether they can CESA from some depth, then they probably should not be diving that depth. It's not that they will ever need to do it, necessarily, but someone who dives regularly to 100 ft/30 m can get comfortable and complacent. Constantly thinking "could I get up from here on a continuous exhale?" will probably make a diver less likely to hit depths complacently.
2. DMs are however a different matter. This is not meant as a criticism of you, but it certainly is a criticism of whoever certified you as a DM. DMs should simply more than a little bit better than a recreational diver. And they absolutely should have the theoretical stuff down to the point that they are not misunderstanding things as badly as you are. DMs are supposed to have instructor level theoretical understanding. But since many instrcutors don't have it, where is one supposed to get that knowledge from?
3. As
instructors, we should all be able to state facts about diving from experience, and not from "Some dude at Scuba Board who might post about diving more than they dive, and repeats received information as if it is personal experience." Personal experience for the physical aspects of diving are key. It makes little sense for an
instructor to have an opinion about what OOA is like if they have never been there or done that, and it is more or less an ethical misdeed to repeat unconfirmed second hand received information as fact, at the instructor level. There is a reason why I have strong opinions that vary from the received wisdom: actual personal experience. I don't trust that someone knows what they are talking about, when I can go verify it myself. And then, I know it not from them, but from me.
There is nothing to prevent people who claim to be 'active' instructors from doing repeating unverified second hand hearsay as fact, though. Because there is very little mechanism (other than actually doing things yourself) to correct those spouting nonsense, and outlying opinions in diving can be either crazy or prescient. It on us as professionals to actually do the things so we can actually see which an outlying opinion is: crazy, or prescient.
There is an ethical issue here about repeating second hand knowledge as fact. That ethical issue can largely be, and usually is, covered up by the fact that recereational diving is mostly safe even when people fsck up fairly badly, or instrcutors present second hand nonsense, that they have no ground for holding beliefs about, as fact. Luckily for us the basic safety factor is what allows people to get away with having such silly ideas about recreational diving.