Can illegal alien leave the country with unpaid medical bills and owing money to other people.

IT will be extremely hard if not impossible to recover this money. You would have to sue the person in their own country as NY courts might not...

An attorney working on the case should address this issue.

Will Border chief rescind my overstay waiver and fraud waiver after CBO cancelled my visa waiver, i'm a Canadian citizen.

You need to work with an attorney. You cannot expect a detailed legal advice on this forum. You might have to reapply for a waiver.

Should I change my name now on my driver's license or should I wait until I get name changed on replacement green card?

It all depends where you need to change your name, with what agency. I would change your LPR card first, I'd say. However, that takes a long time,...

Will I be H1B cap exempt,If travelling on H4(Have H1,But not travelled)

I do not think so. You should consult with an attorney.

L-1B & L2 COS to H1B & H4: Can dependent (L2-H4) travel?

You should present this question before your Immigration attorney.

I was deported after a misdemeanor 8 years ago, but married a USC and i-130 was approved for me, please what are my chances ❓

It depends on the exact reason for your deportation. Consult with an attorney.

Is there any way to know when I will get my I-485 or when expect to?

You should speak with your attorney. Also, you should check processing times at uscis.gov.

My F1 Visa was cancelled without notification from the school. How do I explain this to USCIS?

First, you should consult with an attorney. Second, based on what you presented here and without doing more, it seems you would be precluded from...

I'm on F2 and I applied to change my status to H4 which is approved to start on 10/01/16. Can I switch to F1 now?

Sure, you should be able to do that. However, you really should consult with an attorney.