Hi there! I don't know all of the answers to your questions, but definitely can help with a couple!
We stay in the Boardwalk Villas section, so I'm unsure in regards to room location and fireworks viewing - we typically do a Standard View since we are not in our rooms all that much.
From the Boardwalk Inn, you're looking at about a 10 minute walk from your hotel room door to the International Gateway to Epcot (the "back entrance") You can also hop on a Friendship Boat right on the Boardwalk that will take you directly to the International Gateway, too! It's a nice walk past all of the action on the Boardwalk.
The walk to Hollywood Studios is a bit further, I'd say a good 15 minute walk from the Boardwalk, depending on how fast you go

You just follow the path on the back side of the Boardwalk Inn/Villas under the road overpass and it will bring you directly to the entrance to HS. You can also hop on the Friendship Boat that will take you to Hollywood Studios, too! This boat makes a couple extra stops at the Beach & Yacht Club dock as well as the Swan and Dolphin, so it would be a little more leisurely and take a good 20 minutes.
You definitely can't walk to Disney Springs (DTD) from Boardwalk - but we hopped right on a bus from Boardwalk and it was about a 10 minute bus ride. The main bus stop right outside of the Boardwalk Lobby has the screen with bus arrival times, so you'll have a good idea when the next Disney Springs bus should be arriving.
All in all, you can walk and/or hop on the Friendship Boat to bring you to both Epcot and Hollywood Studios.
I am in LOVE with the Boardwalk and hope you have an amazing trip! We're headed there in October for the Food & Wine Festival!