It's not tone - at least not in the same sense Chinese is a tonal language. Standard Korean does not have tones. Maybe a better term would be intonation: it's similar to how the same English sentence could have multiple meanings, e.g., "I certainly did not see him" vs. "I certainly did not see him."
GP's example sentence would have just two different way to say it, either a plain statement or a question. In either case the pronoun is omitted, so you're supposed to infer it from context.
The great irony here is that the one time I truly started to understand Chinese tones was when it was explained in terms of how English speakers already subconsciously use tones. I think I get what you mean. Correct me if I'm wrong.
Like English, Korean uses tones as a channel for metadata, not as a direct part of the encoding set. You can annotate parts of the sentence with tones, such as marking something a question or highlighting certain information as important, but you can't wholesale change whats being said.
Yes. Older forms of Korean were either tonal or had a pitch accent like Japanese or Swedish, and the original form of hangeul included accent marks. Some dialects of Korean still have a pitch accent.
GP's example sentence would have just two different way to say it, either a plain statement or a question. In either case the pronoun is omitted, so you're supposed to infer it from context.