Can I sign off requirements when my son earns them?

No.   This is a big difference from cub scouts.   In boy scouts, you as a parent will not sign off your own son’s requirements, and in Troop 8 you will not be assigned to serve as his merit badge counselor.  Older boys and adult scout leaders are the ones who can do the signoffs for rank requirements, and your son must use someone other than a relative for a merit badge counselor.  This way, your son gets the full benefit of the experience of working with different adults, and there is no possibility that you can be too easy or hard on him!