My dad got an I797 letter confirming my petition has been approved and that the petition was sent to NVC +?

Yes, as long as the NVC has your father's e-mail address ... they will contact him.

Can I file the citizenship?

It is not necessary for you to repeat your question.

What can I do if I-140 is approved, but I am required to go back for 2 year residency requirement?

You forgot to tell us what EB category the I-140 was approved for.

Which “admit until” date is considered correct, admission stamp on passport or the one on online i-94?

It would help if you told us the date you entered and the 2 different admit 'until' dates.

When renewing my permanent Resident Card there is a question that asks if I have ever been placed in deportation?

Tell the truth. If you got your greencard after your deportation ... and you told INS/CIS this shouldn't be a problem.

Perhaps it didn't have all the necessary government certification stamps/seals.

Marriage Based Green Card (citizen spouse), Affidavit of Support (I-864) Application

Yes, you can have a zero income. Be prepared to show the source of the assets.

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I got an RFE only asking for Birth Certificate. Does that mean I pass for financial sponsorship and and other documents?

Unfortunately, a CIS RFE doesn't always list all the documents that are missing. But, the chance is good.

Filing for citizenship?

You didn't mention how you got your greencard. Most likely you can file now. But, talk to an attorney via Skype for confirmation.

What happens to my immigration application I-485 & I-130 if my petitioner/sponsor/husband quits his job?

If he's not working when you have your interview, you will need a joint financial sponsor.