Yes. A lawyer can charge an hourly rate or a flat rate. If it is a flat rate, the attorney can require payment in full at beginning of services. If an hourly rate, an attorney can require an up-front retainer to bill against.
Sounds like the police used an alco sensor device, not a chemical test. It also sounds like you are not being charged with DUI, only a violation of probation, given a .01 is not a DUI. That could also explain why the police didn't administer a breathalyzer test like a datamaster.
There are several ways to obtain evidence. The most obvious is through discovery--getting Brady and Rosario information from the prosecutor, which the prosecutor is obligated to provide. You also could hire a private investigator to question witnesses and obtain other available evidence.
It means you have a fighting chance of being found not guilty, assuming the pd is worth his or her salt as a trial lawyer. If convicted in Monroe County, you will likely face five years probation. Jail is possible but not likely unless your judge is Affronti or Randall.
In New York, there is no such thing as expungement. Thus, you can't hide previous convictions. You can, however, seek to obtain a certificate from relief of disabilities or certificate of good conduct, which can get you some rights back which you lose with a felony conviction.