Form I-485 Part 3 C

No - not necessary at all to list these associations.

My employer want to sponsor me for green card. What is the process and how long does it take for entire process?

Before responding to your query, we have to analyze the job position and see if it's an EB-2 or EB-3 case.

O-1 to Green Card ?

Yes, assuming you meet the qualifications, you can file it at any time.

What are our options for wife, considering her current O1 expires May 31st, 2016?

She should file O-1 extension and then you should file the I-130 Petition.

In the below situation, should I stay here in US even if my visa expires? Or should I leave before visa expires?

I would strongly advise that you do not leave the USA at this time.

Typically not in a case like this, but whenever an application or petition is filed with the USCIS, one may be subject to a background search.

If my H1b is picked, I have heard it becomes effective from 1st October if that's the case can I travel back to USA on my valid

After October 1st you would need to apply for the H-1B visa at a consulate if you are outside the USA. If you are in the USA then you can begin...

Where do I send my reconstructed I130 petition?

Typically in such a case one files Form I-824.

Will USCIS accept business check?

Yes, as long as it is made out to "Department of Homeland Security".

How much privacy do we retain during the immigration process??

I have had cases where they looked in Facebook and Linked In.