You worry too much about things that your lawyer should handle. If you need to appear in Immigration Court, hire a lawyer and he/she will handle any potential admissibility issues. Judges have law clerks who prepare memos and the judge reviews the memos or the memo and the file before the hearing.
Immigration Judges maintain the record of proceedings in the EOIR. the "A File" is the alien's file with the DHS. Many documents from the A file may be filed into the ROP, depending on the purpose. The rules of evidence are more relaxed in immigration proceedings than in judicial court proceedings, which can be both good and bad for a respondent. Consult with an immigration attorney for advice and/or representation in court.
Your very detailed and well-thought-through post is a great testament to the fact that you need to hire an experienced immigration attorney locally to represent you before the immigration court.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: firstname.lastname@example.org; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
Hearings in Immigration Court are either master or individual. The master hearings are to check status of case, etc. The individual hearing is the time at which the Judge will hear the merits of your case. You can be represented at the hearing at your expense but given the issues you are raising you should invest in legal representation.