how precise do we really have to be about grammar?

[LeTyan]

Dear techers

A Everyone has done their homework.
a Everyone has done his (or her?) homework.

B I don't understand nothing.
b I don't understand anything.

C Me and my friends went to see a movie last night.
c My friends and I went to see a movie last night.

I have heard people say all of those above. But there is probably something tricky about those examples.
As for A and a, I still don't know which one is not ok.

Would saying any of those sentences above make you sound less educated?

[Chicken Sandwich]

NOT A TEACHER

1.

Every / everybody / everyone / everything are singular words, so we use a singular verb.
[...]
But we use they/them/their after everybody/everyone:
- Everybody said they enjoyed themselves (=everybody enjoyed himself or herself)
(English Grammar in Use - Raymond Murphy)

2.

- I don't understand nothing. Double negation. Many people object to this construction.
- I don't understand anything. OK.

3.

- Me and my friends went to see a movie last night. Possible, but it's rather informal.
- My friends and I went to see a movie last night. OK.

[konungursvia]

Some of these non-standard yet common usages do indeed grate my ears, but objectively I accept them as possible and natural within certain contexts. In fact, as for 2., English has been moving in and out of a double negative, along with French, for many centuries (just read Chaucer and you'll see lots of "ne" along with other negated verbs).