Going back to F1 after OPT expires

no you do not to take a class immediately as long as your f-1 status is extended, and SEVIS not terminated.

How long of a sufficient income history do I need to have to sponsor my wife's green card?

it may be an obstacle although your current income will be considered for qualifying but they need to see at least one year of income tax return,...

no you can not be engaged in unauthorized employment of any kind while here on F-1 unless granted an EAD.

PERM Approved but I-140 still pending after responding to the RFE query

delay does not mean reject. it takes time for adjudicator to review your company' response.

PERM Approved but I-140 still pending after responding to the RFE query

multiple posting see your answer in prior post.

My case status shows my GC was mailed to me on June 16. How long does it take to get the card.

it normally takes USPS to deliver interstate mail between 3-7 days. keep a watch on your mail box

Can a person with $4000/month income be a sponsor?

may be it depends on how many people you are supporting and or provided support before, but yes that amount is adequate to support 7 people.

Whats the wait time for a green card holder spouse to get green card and does the wait time changes in a year,how to track it?

currently as of July 2015 about 18 months at the least. you can track the visa bulletin at usdos.gov/travel/visabulletin

How long can I stay in US on H4 after my wife gets her greencard?

you have lost h-4 since her h-1 was adjusted to a resident status, and now are unlawfully present, unless you filed for a change of status to...

Can I apply for naturalization after using my 2-years Re-entry permit and coming back to US?

your facts appear to support it. but consult an attorney before you file.