If someone is on EAD/AP, leave USA for more than 6 mts and I-485 pending, does individual needs to be on payroll to continue GC?

Forget family issue. At least for the principal applicant or welcome and embrace Indian citizenship without US LPR status. You plan is a recipe ...

I live in the UK and considering the Visa Waiver Program. If I go for this can i still take the citizenship test?

I am completely lost as to what you are talking about.

My husband i601 was approved and the consuler wants a orignal court récord for failure to appear

I answered this question of yours in your other post.

My wavier was approved and now sent me a letter wantimg a court récord for failure to appear mom gota sick and was dieing thats

When they grant a waiver, they sort of open a green light as far as the inadmissibility is concerned. They do not issue a clear path to anything....

I have filed an I -130 petition for my husband about 5 years ago and stopped pursuing immigration due to insufficient funds.

You will be way over your head in that one. Hire an immigration attorney. DO not try to do that on your own.

Yes. That person can do that as long as they do not create a management team and start working there.

Can i use a signed statement from the grandfather that he really stay in USA more than 5 years to attached it with N-600K?

Statements under oath are used all the time in immigration cases.

Yes in some branches of some banks.

Is it legal for a non US citizen who is married to a US citizen in there home country to enter the USA with F1 visa ?

Yes, why? It is always legal for him to enter with a valid visa, even when and if you submit an immigrant visa petition. The problem is when you...

How long does it take for I-130 to go from inital review to desition?

About 6 months. You will hear from them soon.