Dependents have never travelled to US before. Can they opt for the dropbox ?

You do not seem to qualify for any dropbox at this time.

yes, you may and the sooner the better.

Yes, you may do so, as long as the new job is in compliance with the OPT requirements,

I agree. Hugely important to consult with an attorney while your recollection is still fresh.

I am applying for N-400 and i am having baby but we are not legal married, i got my green card on F11 bases,

You don't need your uncooperative BF when filing application for citizenship.

N-400 on May 2, 2000. Online status -"Invalid date Case Was Received and A Receipt Notice Was Emailed". what does it mean?

Don't be so impatient - wait to receive it in the mail, then you'll know.

So I need to have an H-1B amendment filed?

Absolutely "yes" to both new LCA with DOL and new I-129 with CIS.

Yes, as long as have a valid EAD and the airline agrees to hire you.

My I 485 was approved but have not received a letter?

You need to contact the 800 number and inquire.

What’s the current income meaning in i864(affidavit of support)? Gross annual income or annual income after deductions?

Before deductions. For all we know after such deductions your income could be zero or less than zero.