The cost of completing the lot split is based on your local area. I would suggest Goggling "Surveyors" in your area, or ask a local Realtor.
In my local market we don't have a great deal of surveying done beause there is very little land that has not been developed. However, in your area I would think finding a surveyor would be easier.
I would also check with the country dept. of Building and Safety regarding the protocol. If originally your land was two parcels, did some one previously merge them? Does you tax bill show two Assessor's Parcel Numbers?
I would assume that the property would retain it's current appraised value. Of course, that may just apply to the land that you hold for your personal residence. It may be that they tax basis would shift on the unoccupied "new" parcel.
You have asked the right questions. Good luck!