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.

1. "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.
2. 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.
3. Cognates: After reading the suggested Wikipedia page, I think that the group (plural you with a word following) are (slang) cognates of one another.

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.

1. "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.
2. 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.
3. Cognates: No, they are not.