"I could care less" is an idiomatic expression. I think it is meant sarcastically. "I couldn't care less" is an example of over-correction.
It's not an idiomatic expression, it's just illogical. If you don't care about something, then you couldn't care less, because you already don't care. But if you care too much about something, then you could care less. In fact, you should, because if you keep caring too much about things you may die of heart attack. :)
The word is spelled 'possess.'
if you were to check a bunch of your claims in dictionaries and grammars you'd actually learn something. I recommend doing that. Not just pontificating on things you apparently don't really know that well (e.g. affect and effect both can be verbs and nouns, but do mean quite different things from each other), the metaphorical use of "literally" is attested from several respected authors since at least a century and a half back. Many grammarians prescribe that "that" be used in restrictive contexts and who/whom/which be used in non-restrictive contexts, which is quite different from the usage rule you propose. Singular "they" is _richly_ attested ever since Shakespeare used it. Your description of the use of "whether" also fails somewhat to catch its actual uses. "Well" is definitely used in an adjectival manner in some idioms in English (especially when discussing health), and "good" does definitely have some adverbial uses, and "except" can also be a verb.This video comes off as something an ignorant knowitall has made. Sorry, not impressed.
Idioms often are illogical. In addition, the kind of sentiment that is expressed by "I couldn't care less" is the kind of negative sentiment that often goes well with a heaping of sarcasm along its side (and in the case of 'I could care less', the sarcasm may be exactly in the form of implying that one actually does care insultingly little, but more than not at all). Now, however, these both full sentences have probably been 'lexicalized' as single meaningful units rather than as sentences whose meaning we understand by parsing them - for most, this means we basically look them up as single words in our mind when hearing them rather than parse them, and for both of them we find the same meaning.