2) Even when we are taught grammar in our English classes, some of the terminology used is different from that that is used by foreign learners. I had an opportunity to test that. I happened to be having lunch with some English teachers at our local high school, and they confirmed that they had never heard the terms "phrasal verb" or "first, second, and third conditional."
3) When we are taught grammar in high school, it usually has a different focus from what is taught to foreign learners. Many puzzling and illogical aspects of English grammar have been absorbed and mastered, intuitively, long before we enter high school.
If we punctuate correctly, it's usually because we read a lot, not because we consciously analyze the grammar of the sentence. To a native English speaker, a lot of the rules of punctuation can be expressed just by saying "a comma shows a short pause, a semicolon shows a longer pause, and a period shows the longest pause." We already have the grammar in our head and we know how long to pause!
P.S. What's the difference between an English teacher and a tiger? Answer: a English teacher has pauses at the end of his clauses, and a tiger has clawses at the end of its pawses. (That's the joke the way I learned it, although I see that nowadays it's been rewritten to avoid the nonexistent but funny-sounding words "clawses" and "pawses.")