This is because the plurals are referred as a singular group. "a lot" is used as a collective noun. The "wrong" example of your last example is also correct. "There ARE lots of cats" would be correct

What great questions! You could move the quantifier to the front 'A lot of those are cats' or use the adverb 'there' instead 'There are a lot of cats'. 'a lot of cats' is singluar thing/idea, so you don't need the plural form of that to be used. As for the second pair of sentences, In the latter you'e referring to two or more people or things twice however I think what you'd like to know is that the pronouns 'it' and 'they' are not interchangeably used when you want to convey a certain message since 'they' is much more limited in its use, furthermore 'it's them' is used informally. 'It's them (over there)' and 'They're them (and will always be)/(and I am me) you may use English like this for emphatic reasons. it's not that the sentences are wrong but need context to seem correct. As for the last pair of sentences, the latter seems to be truncated or a response to a previous statement where 'them' would serve as an adjective. In my opinion you can use both sentences the difference in meaning being 'a thing' and 'people' however in the latter sentence you really shouldn't use that quantifier and pronoun pattern. Hope this helps, Raharuhi

About “It’s them”: Let’s say me and me wife are expecting visitors. The door bell rings. I say to my wife, “It’s them”. It’s a way of telling her that our visitors have arrived. If I said “They are them” my wife would not understand what I was saying. “They are them” would have a completely different meaning. I’m not quite sure in which context you might meaningfully use ”They are them”. “It” can be an “empty subject”. It doesn’t actually mean anything. If I call my wife and say, “Hi, it’s me”. “It” doesn’t mean anything, it’s “empty”.