Yes, it is possible to start a sentence with the word "disagreeing." For example:
Disagreeing is not always the best answer.
Disagreeing is all you two do.
Disagreeing is when two people can not make a common choice.
yes
The noun form for the verbs disagree or disagreeing is disagreement.
Disagreeing indirectly is when you don't think what a person says is right but don't want to say it outright.
Yes, it is.
No, you cannot start a sentence with "no" unless you need to do so. No reason exists not to start a sentence with that word, as you can see. No one will care if you do start a sentence with it.
Yes, I can start a sentence with "Is."
Not really, if you don't mean any disrespect from your decision, than it is merely disagreeing without any offense intended.
Yes, you can start a sentence with a verb.
Yes, you can start a sentence with an acronym.
The opposite of agreeing is disagreeing.
You can start a sentence with "Also"
You start a sentence with whatever word you need to start it with. A sentence can start with "A" if it needs to. A sentence just needs to make sense.