You guys (and gals) in this community are great! I don't think I've ever seen such a helpful and friendly group, especially online, and I just wanted to say I appreciate all of you and the help and kindness you all share.
What we typically call the 'core' is indeed a number of metal pieces affixed together and fastened into the wooden body. The 'heating element' in older Dogs (and occasionally new ones too if indicated) is a resistor (20ohm normally), in new UDs it is (unless otherwise indicated per above) a stainless steel heating cartridge instead. In both cases heat is generated as power (voltage * current) flows through the nichrome wire inside the resistor/cartridge. This flow, over time, eats away at the nichrome wire and it's resistance rises until it eventually fails altogether when it wears all the way through (the wire). As a result of this increased resistance the heating element draws less power and runs cooler. I like to compare this mode of failure to that of a light bulb.. they work, work, work until one day they don't.
Both the resistors and the cartridges can also fail from physical (non-nichrome wear) damage such as overheating, impact, etc. The cartridges are more robust in this regard than the glass/ceramic resistors which is why we switched. That said the resistors are actually pretty damn tough, the cartridges are just that much tougher.
Hope that answers your questions somewhat? If you want to really get into the theory (or like math) of this kind of stuff I can send you an article or two that cover it in detail.
Yep, 20ohm is the 'standard' across low voltage Log Vapes (PD, Zap, UD, HI, Wdz) and they do vary a bit from resistor to resistor. We have also on occasion used some with slightly higher or lower values as needed but they're all close to 20ohm.