Yes, you could. There's no direct transportation from the resorts/parks to Fantasia Gardens as far as I know. When we went in April, we walked to FG. It took around 10 minutes or so to get there from the Dolphin at a slow pace.
Yes, you can either walk or take the Friendship Boat to the Swan/Dolphin. The walk is aoubt 10 minutes or so. The boat is slower, but it is a relaxing ride. The Friendship boats load to your left as you exit the Studios.