So while BTC Satoshi's will always be 100,000,000 - other coins Satoshi's will vary depending on their VALUE to a BTC Satoshi. Correct?
No.
almost all the altcoins and also bitcoin have 8 decimal places which has a meaning. it means they can go as small as 0.00000001 number.
in bitcoin this number (0.00000001) which is the smallest meaningful number with bitcoin is called satoshi in honor of the creator.
other altcoins like litecoin, ethereum, Doge, XMR, ... have the same rule of numbers meaning they can go as small as 0.00000001 ltc, 0.00000001 eth and so on. these don't have any names but some called litoshi for litecoin.
the value is the same as anything else it is 0.00000001 * price of that altcoin.