Renting your home is a great option until the market stabilizes and that same agent should be able to give you comparable rental rates in your area.
As for how much agents charge for rentals, there is usually a standard amount, but can't discuss it because in Florida, it would be considered "price fixing".
The agents get paid upon signing of the Lease agreement and it does not involve any property management. (some agents also offer single-property manament for their customers).
The tenants will be responsible for getting utilities in their own name (what the Lease agreement includes is negotiable).
If eviction is necessary, you will have to hire an attorney or the property manager (if you hire one) may be able to guide you.
The liability will not rest with the real estate professional, that's why they will recommend to get a credit check and credit reference before the Lease agreement is signed.
Rentals of SFH's vary depending on your need - short-term rentals of 3-4 months are usually more expensive, one year rentals are more common.
The rental market is HOT, which means your home, if priced correctly, should rent quickly.
Take a look at the link attached to get my opinion on the rental market. Sometimes renting a property that has been on the market for a while will help, because it will let it cool off from the market.