Surface rights

Do I have any rights if I don’t own the mineral rights to my property? Do I have to let them access my property? And if I do, can I say where to access it and should they compensate me for the access road?

Also, do they have to stay so far away from my home?

Yes, you have some rights depending upon which state the property is in and whether prior owners not only reserved the mineral rights but also the right to access them. Speak with a good land attorney in your area.