What should to do to get SS and EAD ?

They would need someone to petition for them. Do they have any US citizen children over 21 or siblings with status?

Can my children apply for immigrant visa through the US consulate overseas even if PD is not yet current?

Until the priority date is actually available processing is not allowed.

There is a possibiity that I may move to a different state and be unemployed. Is it okay that I am on EAD card and unempolyed?

You are permitted to work at your discretion.

You can check your status at USCIS.gov. The process takes about 90 days.

Can I open a business (sole proprietorship or single-member LLC) and draw income or profits from it?

You can open a business but unless it hires you as an h1b you cannot draw income.

How do I start fixing him papers and where do I start?

Assuming you have status you file I-130 form proving your relationship. Assuming he came illegally you will need to file for a waiver and prove...

Because my I-130 was approved is that mean I don't have I order removal?

The only thing an approved I -130 does is find that the petitioner and beneficiary have a valid relationship for immigration purposes.

You cannot sponsor him until you decide to marry and then you can do a k1 or K3.

What is my current status?

Your current status is none. Why do you ask?

No Green Card Interview?

Yes that would mean the interview has been waived.