You will need to sign a letter of attorney at notary office so another person can search on your behalf in archives. If request is made directly, then around $750 genealogical search for a single family. I don’t the letter will be needed. Queue is about a year long. Maybe quicker in Grodno than Minsk. But I wouldn’t be sure. I don’t think all money have to be paid upfront. In your situation, I’d have chosen to use services of the archive even I had to wait for a year.