How do you demonstrate to USCIS that you have completed your 3 years of J-1 waiver in H-1b status with your employer

Your H-1B Notice of Approval. You income tax returns. You pay stubs. Etc, etc.

Is there any hopes for illegal immigrants in 2011

I do not think so. Please see

You can't force him to sponsor you for a green card. Is there something wrong with him? Abusive? Please see

I filed an I-130 for my brother, his wife, and his son in 2002

When the I-130 is approved and sent to the NVC, inform the NVC about the new child. No need to start over.

How is your time counted in J1 waiver for 3 years.And who will issue the letter of completion to USCIS

You need to demonstrate that you were employed in H-1B status for 3 years after your J waiver. Please see

Can a current sponsor be removed by filing additional I-864 form?

No Please see

They may ask you about it, and you should bring the record of conviction to your interview, but it should not affect your eligiblity for...

Will this hurt our chance of receiving a K1 visa?

It would have no effect on his ability to immigrate to the U.S.

Can my husband ligalize

Did your husband enter the U.S. legally? Or is he eligible to adjust his status in the U.S. under section 245(i) of the law? If not, you may want...

How do i respond to NVC for AOS while i am in US legally on J-1 waiver and i have an approved I-130 petition

I agree with the above answer. For additional information, please see