You can always file an incomplete application. However it will result in a delay in processing as you will get a request for evidence (RFE) seeking the birth certificate. Your adjustment application cannot be approved without the birth certificate or a legitimately documented non availability of it.
Since it was filed early, namely, before April 1, USCIS can reject it and return your packet back to your attorney. However, since it was a weekend, they may consider it as filed on next business day which is April 1. There is no clear answer to your question.
Considering that USCIS will consider petitions filed all week towards a tentative lottery, you may not know until next week how they proceeded with your petition. In addition, duplicate filing is not permitted; your employer...
You have 2 choices - have your case reviewed by an attorney for his/ her opinion whether you filed a good convincing bona marriage case with appropriate documentation OR risk another interview of not convincing the Officer. If the latter happens you are likely to pay more towards refiling or challenging the decision.
The USCIS may visit the bona fides of marriage when you apply for naturalization since you got your green card through marriage to USC. Divorce, by itself, does not automatically cause termination of residency.