Your south of where the restaurants are. Trolleys take awhile and traffic is at a snails pace especially during the winter tourist season. Uber might help. I wouldn't recommend walking either as it's quite a walk to find food. The view is great though and it's relaxing!
You do need a car, but be aware that Estero Blvd gets quite congested around Fort Myers Beach at dinner time.
Yes, you'll want to rent a car.
Yes, if you are staying at Carlos pointe there aren't any restaurants in walking distance. Plus, it's at least 30 minutes from the fort myers airport.
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