I built a 23' x 13' mono roof for a shed with a good grade. First question is if the rafters are at 18" apart should I use 5/8 or 3/4 plywood, what length nails and can the same nails be used for the sheathing, felt, and drip edge? The shed is in Florida.

5/8 is fine. Why 18"?, throws all your sheathing measurements off. Standard is 16" centers, always bearing at 4 and 8 ft. Nails serve different purposes. No, you can't use the same nail. Sheathing should be nailed with 8d cement coated sinkers. Felt can be either stapled down or with plastic washer nails, I use a hammer stapler. Drip edge can use the same nail as what you will use for the shingles, make sure to nail the drip edge into the roof rafters. HOWEVER. Note that FL is pretty specific as to construction practices due to windstorm. You might want to talk to a local building inspector.