not a teacher
As a basic tool to go by for formal and informal, use 'X and me' for informal, casual talk and 'X and I' for formal and professional use. (#2 and #3).
I never encourage learners to use "X and me" (as the subject pronouns), even in casual, informal speech. It's far too easy to get so used to using it that people forget the correct form.
For any learners who struggle with this, here's a trick to help you work out whether to use "I" or "me" as a subject pronoun - remove the other person from the equation and see what you are left with.
May and I were playing in the park.
Remove May from the situation and repeat the sentence, keeping the pronoun but following it with the correct verb form.
I was playing in the park. :tick:
May and me were playing in the park.
Remove May from the situation and repeat the sentence, keeping the pronoun but following it with the correct verb form.
Me was playing in the park. :cross: (I'm sure most learners would recognise that that's wrong.)
The same rule applies to object pronouns, an area in which lots of native speakers get it wrong.
Helen gave a slice of cake to May and me.
Remove May from the situation and repeat the sentence.
Helen gave a slice of cake to me. :tick:
Helen gave a slice of cake to May and I.
Remove May from the situation and repeat the sentence.
Helen gave a slice of cake to I. :cross: (Again, most learners would recognise that that's wrong but, like some native speakers, don't think about it that way and incorrectly use "I". Some native speakers think it makes them sound more formal/professional/well-educated. They're very wrong.)