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.
Yes, it is.
Disagreeing indirectly is when you don't think what a person says is right but don't want to say it outright.
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."
Yes, you can start a sentence with a verb.
Yes, you can start a sentence with an acronym.
Not really, if you don't mean any disrespect from your decision, than it is merely disagreeing without any offense intended.
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.