How do I make appointment for 1yr old male nueter?what is normal cost?

You can setup an appointment by going to: https://www.ddfl.org. I took my cat to get neutered which was free of charge, not sure about dogs.

Cats are free dogs are 50 dollars on neuters and spays

I would be very diligent about who will be staying my female dog

Usually their website but they are booked. You can always try planned pethood