you can tell i'm tired, i voted "Yes" but i meant to vote "No".
honestly, no. i study languages myself, and i find it really helpful when native speakers of the languages i study correct me.
but i can definitely see how it can come across as rude - it all depends on how it's phrased, and the tone you put across.

It depends but generally yes

"Out of the two choices"

If you do it in the Grammar Nazi manner, then yes that's rude.

Not at all. If you want to speak or write in English, do it correctly. The same is expected for any other language.