Hi Timothy, this is something I've been searching for too. Here are two PDFs I managed to find which were pretty interesting:
I can give you my thoughts on a couple of the example questions you mentioned.
2. This has been baffling me too. A closely related question is, if with TIG you get more penetration on DCEN why with stick do you get more penetration on DCEP? Can't remember where I heard it but the reason the heat is biased in the direction of electron flow is that the electrons have a much higher velocity than the ions (eg Argon ions in TIG) travelling in the other direction. The velocity of the charge carrier is the main factor in how much energy it delivers when it makes contact with the workpiece or electrode. One key difference in stick compared to TIG is that, in stick, the electrode is travelling in droplets onto the workpiece. So this 2/3 of the heat which is going into the stick rod on DCEP still ultimately ends up travelling to the workpiece in physical droplets. None of that answers your question but I hope its helpful or thought-provoking.
3. One thing I've noticed about puddle size with TIG is that it doesn't appear to be depended on the electrode diameter. If I weld with the same settings with a 1/16" or a 3/32" electrode I get the same puddle width. This observation surprised me but it has been my experience.
In terms of AC frequency, I wonder if this is to do with the shape of the wave. Let's say you are welding with a classic sine wave. If you lower the frequency you stretch that wave out sideways (if you were looking at it on a graph). Any point on the wave represents some amperage, with the crest of the wave being the actual current you set on the machine. If you stretch the wave, does the machine spend a more time on average at a higher current? I guess it depends on how the geometry of the wave actually changes, how the circuitry does this. On a square wave where the switch from the negative to the positive side of the wave it theoretically instantaneous, I can't see why frequency should affect heat input.
Another thing I've noticed from experience is that if I TIG weld aluminium sheet on pulse without filler, it doesn't work nicely if the pulse frequency is too high (too high = for example pulse duration of 0,1 second, background time 0,1 second). The puddle doesn't appear to have time to develop or, specifically, the oxide layer doesn't seem to open up. I don't get that shiny puddle. So cleaning action appears to me to be dependent on time as well as current (aside: Mike Zanconato on the welding tips and tricks podcast said that cleaning action seems to be dependent primarily on current and less on time. Not saying this isn't true). If you lower your AC frequency you are giving more time for cleaning to happen during each cycle which I think can allow the puddle to open out. That of course only affects the width of the puddle, not its depth...
4. Addition of CO2 to the shielding gas for MIG (MAG) welding reduces surface tension of the puddle which gives the bead a flatter profile and smoother toes. I don't know the physical mechanism of this. It also improves heat transfer into the puddle. You can MIG carbon steel with straight argon and stick two pieces of metal together but penetration will suffer significantly. I also don't know the mechanism of this but perhaps its similar to helium with TIG.
Helium has a higher ionisation potential than argon. This is why arc starts with helium are worse because the required energy to ionise it is higher but it also means that the Helium ions carry more energy and deliver more heat to the work
Here's another thing while I'm at it which I recently learned about shielding gases. Linde recommends Argon with an addition of Hydrogen for purging stainless. The explanation for this is that any oxygen "stuck" to the microscopically rough surface of the stainless steel, which didn't get pushed out by the purge gas, will preferentially react with the hydrogen rather than the molten steel.
Another thing you might enjoy reading about is "sputtering":
I believe this is the actual mechanism of cleaning action on aluminium. The oxide layer is bombarded with argon ions which sand blast it on a tiny scale. This would also explain Zanconato's observation that more amps = more cleaning = more argon ions slamming into the workpiece and opening the oxide layer.