1)
( On my trail bike project I replaced the battery with a Mallory 8.9 uF 16V - 20V cap ...One of the drivers here was to stop the continuous battery killing 16V overcharging.) Mission accomplished, overcooking battery replaced by a capacitor that won't cook off.
2)
" If a cap was an open circuit to DC, it wouldn't charge. " A capacitor
stores charge as a static electrical field in space. Walking across a new nylon carpet can make you a capacitor, storing charge until you hit the doorknob. Full charge & discharge times are very short. Adding a resistor creates a definite time delay, and RC circuits were routinely used for timing functions until digital electronics created a better way.
3)
" Regardless of what you call it, impedance, or ESR at 120hz as the manufacturer specs it, the internal resistance of your Mallory is greater than the internal resistance of a motorcycle battery in good condition. "This is apples & oranges. Apply a DC voltage across a cap with your VOM and it charges up until it's at "full capacity" for the voltage applied, then current drops to zero. E/I = R, E/0 = undefined, infinite. Infinite resistance.
Resistance is a DC function. It'll stay that way until you apply enough voltage to blow it up. AC current flow applied across a cap is limited only by the impedance, the frequency dependent DC resistance analog in an AC system. Those
impedance values for caps are the numbers you so correctly pointed out. The fun begins when you look at transformers. The low side coil resistance might be 0.05 ohms, high side 0.5. Put 120VAC across them and you don't see 2,400 amps or 240 amps, maybe 0.1 amp AC. Reflected impedance is the voodoo that makes that work. Short one side, apply 120 to the other and watch the smoke as impedance goes to near zero.
4) As far as Community College Electrical/Electronics, it's a good place to experiment and learn. When you get to the point that you can accurately describe why a single phase motor turns, why a 3-phase motor turns, the difference between AC & DC relays & why, why and how thermistors are used, play with a variac for awhile, learn about step up/step down transformers, inductive phase shifting & how it works, capacitive phase shifting an how that works, maybe look at the relationship between field strength & power factor in a generator, play with relay style controls, figure out PLC driven controls, build some RC & LC circuits, burn up a few transistors & resistors, maybe then you won't be so dismissive of solid basic knowledge, idealized models and simple analogies. Quantum electrodynamics describes the odd goings on at the atomic level as to why all this stuff actually works. That's far beyond most of us, and largely unnecessary just to repair or build functional devices, so we're left with basic knowledge, idealized models and simple analogies.
https://en.wikipedia.org/wiki/Quantum_electrodynamics.