'Best way' (and I rarely say this) is Uber/Lyft. It's just not overly convenient to get to Fantasia from most resorts.
Another option is to take a bus to DHS. Friendship Boat to Swan and walk over to Fantasia from there.
Yes, you can walk from Fantasia Gardens to Epcot - International Gateway. It is 0.7 of a mile.
Another option we've done is after mini golfing we've crossed over to the Swan and taken the Friendship Boat to International Gateway. After a long day with lots of walking, the boat was a nice way to cut down on some steps.