Is the חאם before the rest of the sentence the more formal way to say it?
Do you mean האם? if that's the case than yes that's the more formal way to say it.
How is חמוץ pronounced?
It is pronounced "Ha-mu-tz".
Is "האם" some kind of question particle?
Yes, it signifies a yes/no question, and in spoken Hebrew it's not really used. The question-ness of the sentence is conveyed with the question mark or the intonation.
מה ההבדל בין התפוח חמוץ סימן שאלה לבין התפוח חמוץ?
What does חאם mean?
Pronunciation (using approximate English transliteration):
Does ק serve as a another letter to be pronounced along with yes?
No. But, as I learnt from my 8 years old son, children these days omit the /n/ in כן, and pronounce /ke/. Drives me nuts. If you are not a child, don't do it (-:
without keyboard cannot make it
The Hebrew is one of the least enjoyable courses. Needs way more of the language spoken in each course. Otherwise, very difficult to learn how the letters should sound.