I feel that
i miei amici e io
is a bad translation.
What would be the grammatically correct way to say it?
"My friends and I" would be generally translated as "Io e i miei amici", " I miei amici ed io" is also correct.
Ngram Io e i miei amici vs I miei amici ed io
"I miei amici ed io" is the better translation that you can do. Please, note two things: