Yes and yes
Its a very quick walk. Just across the bridge and down the hill from Boardwalk. Its before the International Gateway entrance, virtually right across from the Epcot Friendship Boat docks.
As mentioned, if you have an ADR at Boardwalk, you should be able to park there. Otherwise, Disney expects those checking out the Skyliner to park at DHS.
No. All of the stations are outside the park entrances or at resorts. If you ride from the International Gateway entrance, you will stop at the Riviera station and then everyone will be required to disembark at CBR, which is the main Skyliner hub. From there, you can either ride the line to DHS or ride the line to Pop/AOA, although AOA is closed right now. If you want to just go back to the International Gateway station, you still have to exit but then can just jump back in line and get back on.
Yes. The DHS one isn't terribly far either, just a bit past the Friendship Boat docks, but I think the Epcot/International Gateway station is closer. Plus, that line is a longer ride with more to see than the line from DHS.