Bad English- .... than me (reads books) is not correct. It should be. "She reads more books than I (read books).
So many people in Britain now say 'than me' that 'more than I' sounds incorrect! and pedantic., you'd have to complete the sentence.
Seems that I may use "do que eu" and "que eu" interchangeably ?
Yes! In comparison use "que" or "do que"
Could it be "Ela lê mais livros que mim" ?
No. Only "eu". I = eu, me = mim
When should we use 'mim' vs 'eu' ?
Use mim after verbs and prepositions, and "eu" as subject pronouns.
It says "than me". No "than i do" . Than me should be correct.