I'm just going to hit a few random points and I'm leaving a lot out intentionally because the post is way too long as it is.
Read a dozen college/university level books or a vocational one like Delmar's and you'll find a chapter covering ohm's law, power and energy in all of them under the same umbrella. Look up the ohm's law calculations and every chart includes the power calculations. You'll have an easier time finding Bigfoot than you will "Watt's Law" in any book at that level.
Though some high school teacher's slide show messing up terms doesn't even raise an eyebrow. I at least understand where that bad knowledge is coming from and even forgive it...
...a teacher changing things up in an attempt to make it easier to learn. OP got screwed by the education system there.
Try going to electriciantalk, eeweb or the eeevblog forums and see how "Watt's Law" flies there. Those guys can use some entertainment.
Here are some of the most simplified and straightforward explanations I've ever seen on the subject of DC-DC converters,
Boost Converter and
Buck Converter. That guy just does a fantastic job of it. Just keep in mind these are about as bare bones as it gets. If you want to take it further, I'd recommend watching Dave Jones' EEEVblogs, then maybe picking up Brown's Power Supply Cookbook, a book written by a practicing design engineer for practicing design engineers. Of course a few prerequisite books covering general electronics would be necessary. Getting into VW/VV mods generally requires going well outside standard specs for most PMIC (power management integrated circuits) chips and require advanced knowledge.
As far as mods being able to draw more than a battery is capable of, sure its possible i.e. a budget priced product like anything
eleaf (or it may very well have a good PMIC battery chip for all I know...I've never tested one) might over draw from a battery, but most quality boards incorporate a PMIC battery management chip that prevent the
mod from overpowering the battery, put in a 10A battery and it will limit the
mod to drawing 10A from the battery. They're dirt cheap chips and easy to implement. P Busardo and others have demonstrated those capabilities in practical testing on some mods like the DNA40 and SXMini, it would be a simple thing to test for.
While isolation from battery to load is theoretically possible, isolation typically increases size and costs of a DC-DC converter from 120% to 250%, also peak efficiency suffers by up to 10% depending on topology chosen so it will never reach a peak efficiency even close to 90%.
When you consider most mods are designed to be as physically compact and efficient as possible with peak efficiency commonly reaching the mid to high 90s, it places them squarely in non-isolated buck, boost and buck/boost circuitry templates.
DC-DC converter theory and some basic battery management 101 that is as plain as day to anyone familiar with the subject. The very minimum knowledge I would expect of anyone handing out professional advice and making definitive statements.
There's nothing wrong being a professional and saying so, there's nothing wrong with handing out advice, even getting it wrong when going out on a limb and making it clear that it's an educated guess. And of course the honest mistake can be forgiven.
But when someone runs around making definitive statements of fact as an authority, stressing they are a professional repeatedly, while being consistently so far off the mark across the board that its almost comical, it leads to some unflattering places....