The notarized statement/agreement means nothing when it comes to family court. It may possibly be evidence of your wife's involvement with your children, but it is not a binding in any manner. Definitely go see a family/ divorce lawyer.
First, congratulations on working on your marriage and deciding not to pursue the divorce. As you said, your case was begun in July 2016, so it is likely that the judge issued a continuance because she does not want to make you restart the process if you wanted to continue the divorce. Filing a motion to dismiss or contacting the court (both you and your husband) and informing them of your decision should prompt them to set it for dismissal again soon and then dismiss the case.
The marriage license you applied for is not likely to come up, but even if it did, it is simply answered and should not affect your application for a green card. Should you bring it up in the interview - as it doesn't relate to your current marriage, I personally would not bring it up.
The most important question about your application is your marriage - they want to know for certain that your marriage is real. Questions that will be relevant is how did you two meet? How did you fall in love and decide to get married? How were you in the US - student visa, work visa, visit visa, etc - when you got married. Were you married close in time to the expiration of your visa? Such questions are not conclusive, but they will look for circumstantial evidence that your marriage might not be real.
If there are other things that are a cause or concern, then you should seek an attorney to assist you with this..
Based on what you've said, you've defaulted on your obligations. As such, a review of the agreement is best to determine if this would cure the default or not. It is likely best to contact the owner and ask if you can cure the default by doing so and avoid eviction. If they agree, make sure to get such agreement in writing. Otherwise, contact an attorney to review the lease to determine if you have other recourse.