I have a doctorate, and I also live in a city. None of which makes me think I can be a better journalist than a professional journalist like yourself. An attorney that does a good job leaves you unaware of the pitfalls of these applications because they already know the common pitfalls and mistakes related to these applications. For most people, the small expense of an immigration attorney is worth the assurance that it is done right. If you would like to discuss your case, we can help you in...
If you don't trust your lawyer, why did you hire them? But what you are describing is correct. There is no filing fee for Asylum, fingerprints are scheduled later by USCIS. There is a filing fee for the work authorization, but that is filed 150 days after the original Asylum application.
If you have filed for asylum, you become eligible for work authorization 150 days after the filing of asylum. If you marry the US citizen, they can petition for you to get residency completely separate of your asylum case.
We have been able to ask the immigration judge to give us long continuances in such cases to wait for a decision from USCIS. If your claim is very strong and it is obvious that USCIS will approve, the judge can administratively close the case.