Origin of "you lot" and other plural forms of "you"
The answer to your second question is ‘no’: they are not cognates. Cognates are words descended from a common etymon; that is not a correct description of you lot, you all, y'all, yeuns, you guys, you folks, etc. (except for you all and y’all, of course). They are phrasal extensions of the bare pronoun you created to make it explicitly and unambiguously plural. For some speakers they’ve been fully grammaticalized, meaning that they’re no longer perceived as phrases but are single lexical items. This is especially true of y'all and yeuns for speakers of the varieties that have these two pronouns. My impression is that some British speakers have lexicalized you lot; I’ve encountered Americans who definitely seem to have lexicalized you guys (typically as y(ə)’guys), though I’ve not been in a position to investigate this scientifically.
I don't have first hand familiarity with British English. However, there are sufficient counterparts with American usage, particularly in the links provided for clarification, that I'll try to respond.
- "You" is both the singular and plural form of the word. "You lot" or "You all" seem neither elegant nor accurate, as the plural form of "you" remains "you". "You lot" and "you all" are redundant. I wouldn't even consider them colloquial usage. Slang is more descriptive.
- Regarding the increase in usage over time: Yes, it did accelerate sharply from 1960 onward. Note though that the trend has reversed. The expression may not have entered the corpus, as usage rates dropped and have returned to levels observed (via your helpful link) last seen in the early 1980's.
- Cognates: No, they are not.