This shed is added to a metal carport and has exterior walls, dirt floor no interior walls & no ceiling. I will be using lights & outlets. Is this acceptable or must I do something different.

You should drill holes through the rafters to thread the romex through. This keeps it "tidy".

No you cannot staple cable to the bottom of framing members.

Running boards need to be attached to bottom of joists then cables can be stapled to the running board.

This prevents the cable from being used as a hanger.

Where is this shed located, state, town?

I live in *******, Georgia. Could I run the wire next to the 1x4" lathing on top of the rafter and staple to the side of 1x4 lathing or top of rafter. Metal roofing on lathing. Don't want to drill in rafters, have my reasons.