Why the word 'Do' is omitted here?
We usually say: How do you feel about it?
and also: Could I ask you how you feel about it?
and why not: Could I ask you how do you feel about it?

Why the word 'Do' should be omitted in the second sentence?
Is it because that sentence has two part [Could I ask you] + [how you feel about it]?

Question

Why the word 'Do' is omitted here?
We usually say: How do you feel about it?
and also: Could I ask you how you feel about it?
and why not: Could I ask you how do you feel about it?

Why the word 'Do' should be omitted in the second sentence?
Is it because that sentence has two part [Could I ask you] + [how you feel about it]?

Answer

Yes, the main question is not "how do you feel?", but it is "could i ask that?".

Answer

It's not omitted, it shouldn't be there. You only add it when asking a question. The sentence IS a question, but only because it starts with "Could I...". "How you feel about it" acts as a noun.

Answer

Yes. The sentence has those two parts and the second part acts almost like a quote of what was said. It really, ought to have a comma after "you".

Can I ask you, how do you feel about it.