The third person singular (he, she, and it) form of the verb to do in the present tense is does. Therefore, "sun doesn't shine," is the standard English form and the only form acceptable for English students.
Quite often, native writers will use non-standard dialect forms of English to add emphasis or "character" to their writing. This is especially true ...
It is an informal AmE usage:
Don’t vs doesn’t
Don't is occasionally used in American English speech and in historical writing as a contraction of does not (as in, "He don't know where he is going."), but this use is now considered improper and should be avoided.
Interesting Q! I've used 'the FAQ' for decades. I've always pronounced it out by the letters. "The F A Q", rarely by the words. The Frequently Asked Questions are sometimes useful, often not.
Occasionally, "Just read the FAQ" is indeed a way of telling someone that they haven't done their due diligence, especially in tech, similar to RTFM. "Read The Fine ...