1. Yes, your understanding is correct, it means "I knew it!" . The "и" gives more emphasis to it.
2. Завтракать means to have breakfast. It's a 1st conjugation type verb.
3. Занят is a short form of an adjective.
4. correct
5. Only I think that you haven't eaten anything today.
6. correct
7. "А что?" is like "Why? (why do you ask?)
8. Looks like some misprint, it's not a word
9. "Дня" is the Genitive form of "день".
10. Yes, it means "first time", but it's not an adverb. "Раз" in your sentence is a noun, it means an instance .
11. Это круто! = That's cool!