How bad is it to file for an extension of B-1 in the US while waiting for I-130 approval?

She is eligible to file for adjustment of status on Monday October 1st. The second chart in the visa bulletin controls for this circumstance.

Yes. You'll have an unrestricted work permit. Unless a job requirement is to be a US citizen, you're all set.

If you changed your address with USCIS AND, when you did it, you indicated that you had this pending case, then you should make an infopass...

H1b expiring in a month, shall I ask for premium processing?

As long as you file before your stay expires, then you're fine. I would do premium processing if you're going to have a need to travel overseas...

I-360 has to be approved before you can file for adjustment of status.

I went to my citizenship interview yesterday and the interviewer requested documents showing proof that i supported my daughter?

Your moral character for the 5 years leading up to the date of the application is considered. Therefore, if your child was 23 or older when you...

Can I file I485 and I130 together while I am in the US with a recently cancelled J1 visa?

There may be no issue at all. Only if the J visa stated that you were subject to the two years foreign residency requirement would you even need...

She is eligible so long as you're a US citizen and she entered legally (except as a crewman). INS is now called USCIS.

Question about approved I-130 with current status F1 visa.

Your priority date is not current. If you're in the US legally when the priority date does become current, then you can file these forms. Until...

Will there be complications on my green card process?

As long as both marriages are/were legitimate (true marriage for love and living together) then you should proceed.