A lot

Hello,

A. The word ' lot' works as a determiner, pronoun , noun and an adverb. When it is a determiner, its form becomes ' a lot of' or 'lots of'.

1. I have a lot of time. OR I have lots of time.

2. She has a lots of books. OR she has lots of book.

This 'of' construction reminds me a pronoun like 'some of ...', so I get confused.

Shall I think ' a lot of' a single word like 'many/much' in the case of determiner?

(B). When used a pronoun or an adverb, its form is 'a lot' or 'lots'.

How to use 'a lot ' or 'lots' as a pronoun is not clear to me?

(C). When used an adverb, its form is like ' a lot' or 'lots ?'

1c. I miss my family a lot.
2c. I miss my family lots.

Could any one explain the different aspect of the word 'lot'?

Thanks.