I don't mean to be flippant because I think there is a lot of helpful advice on AVVO. But this is an area that is highly specific to the needs of the employer and very complex. Anyone attempting to do this without an experienced attorney is making the same mistake as someone trying to do their own root canal. Get someone who knows exactly what they're doing, understand it's going to cost $$$, understand there will be a protracted delay, but get the facts first.
What's the point of the story about the friend and getting caught at the border, and the "scratched out" passport? Are you trying to say that your undocumented alien husband left the U.S. and then was prevented from returning? If that is the question, then the answer is maybe. It would depend on whether or not he had any other grounds to prevent him from returning to the U.S. I would assume that he had lived in the U.S. for more than a year he would be subject to a ten year bar that could...
It sounds to me like your father was removed for committing an aggravated felony (trafficking). After 1997, when you are deported for an agfel you are permanently inadmissible. However, it would be worth the price of a consultation with a specialist to have a thorough review of your dads case. I'm sorry!
You do not need to pay the $1000 (for a bunch of reasons we don't need to get into here). He does not have to leave and yes, you can file the I-130 and the I-485 concurrently. As for whether or not you need a lawyer, as a lawyer I would say enthusiastically "absolutely".
An I-601 is the form for the waiver(s). I'm not sure why your lawyers would tell you that you didn't need an I-601, but you do need two waivers. I think this is an attorney/client communication snafu. Go back to your lawyer and try to get them to explain better.
Drive safely and ALWAYS obey the law. But if you get caught driving without a license it will not impact your naturalization case. However, you should take your ticket in to an attorney experienced in traffic violations, Craig Kinney, for example, and have him take care of the ticket, usually if you can get the lawyer to buy you enough time to be able to produce a valid license, the courts in Nevada will just dismiss the ticket.