My suspicion is that you heard what you wanted to hear when you had your initial discussions about your DWI matter with this attorney. To answer your question from a slightly different angle than my colleagues, if you don't pay your bill, some, but not necessarily all, of the following unpleasant things could happen:
1) The attorney could sue you, and if successful, obtain a money judgment against you. Your stated intent to lie under oath will probably not bode well for you, as it is a crime...
Please refer to information posted on the New York Department of State's website regarding the the real estate salesperson license:
From this page, there is a link to the relevant sections of the laws applicable to the real estate salesperson license.
Your judgment likely only contemplates the monetary relief you asked for in your petition. When it refers to costs, it typically refers to statutory court costs (like the filing fee).
Recouping cleaning service expense is something that would be covered by your lease. Depending on the terms of the lease, you may have the right to seek a separate money judgment in small claims court.