First of all, see "Prepare for your road test". Then the fee for up to two road tests for a non-commercial license is included in your $10 driver license application fee. The earliest date is within three to five weeks.
My temporary learner permit is without a photo... is this a problem?
You must show a NY State photo driver license or a NY State non-driver ID Card, Photo documents from other states are not acceptable. The vehicle must have functional seat belts, headlights, windshield wipers and other equipment, a front passenger area and a seat belt free of debris, clutter or debris that may stain or damage the license examiner's uniform, and a driver's door front passenger that can be opened from inside the vehicle.