It can be understood by a native English speaker but sounds less natural than "We are all teachers."

When one looks at the verb "to be", one would almost believe that "We all are teachers" would be wrong. This is because of the conjunctions (I am / You are / He,she,it is). Together they are the verb and forcing a word between of the syllables of the verb does not seem to be correct.

In Chinese, 都 is put after the subject, not after the verb.

The english is correct. Yes

I am not sure if the grammar is correct (English speakers please?) but "都" can be either "all" and "both."

I think it may have to do with the sentence not specifying how many people the 都 is referring to, as in, 2 or a number bigger than 2. So maybe it's supposed to be assumed as "all" as opposed to "both". Although since the meaning is kind of ambiguous, I can see how both answers should be accepted.

I wrote "We are both teachers." and got it correctly.

都 can be used not only by two people/things, but also more than 2.

This is not a common word phrasing in English at least not most American English. We would normally change the sentence to "Both of us are teachers" referring specifically to 2 people.

That could be a option

我们 can apply to more than 2 people, it could be referring to a group.

Sorry, i write this comment totally wrong :) I am trying to say i English is not my mother tongue. (Actually it's quite obvious :/ )

"Both of us are teachers" (using the plural of "teacher") is correct English. I don't know if it's a correct translation of the Chinese sentence here.

That is not correct English as your sentence does not contain a verb

you are missing '是‘ from your translation