I'd say Beach Club a is slightly shorter walk to Epcot (maybe by 5 mins) and yes, Boardwalk is a closer walk to Studios than Beach Club. We cut through the pool area if we are going to the Studios instead of walking all the way down the Boardwalk to meet up with the path. It's probably faster to ride the boat from the Beach Club.

The refillable mug station is in the store, where you can also get lunch sandwiches, gelato, breakfast sandwiches...you can also have them fill your mug at the bar at the pool.