Based on my explanation above, will I be denied from citizenship ?

I do not believe that the arrests more than 5 years ago will be an issue.

Parent on B2 (10yr visa) currently in the US, will travel back in April. Can US citizen file for her GC, 130&485 together?

Yes it can be filed. She will also have to apply for advance parole for her to be able to travel outside the USA. That can take close to 4 months...

What to write on Part 1: Uscis Status on form I-485?

"I-539 pending" but since you are marrying an American, I assume, what you put down will not jeopardize your case.

Marrying a U.S citizen for green card, who previously sponsored another man for green card through marriage

It would not be an issue as long as you can establish that you have a bona fide marriage.

If a petition for a visa is ready earlier than my restriction expires , can I wait for a while to apply for visa?

You can definitely begin working on the case but I wouldn't file until the 2 years are up.

You should seek to file a new P-1 petition with the private golf course. It appears that you have the necessary P-1 qualifications.

If she never dealt with an I-94, will that come in the way of the I-130 process?

Did she ever receive any stamp in her passport? Canadians do not get I-94s when they enter the USA

I always tell my clients that an experienced attorney can "expedite" the process by making sure that all is done correctly from the start.

Yes - LCAs do have expiration dates.

Can an Irish Dancing Teacher from Argentina, get a P / O visa to teach in New York?

If it's culturally unique then P visa would be most suitable and can be filed while in the USA.