Walking from Epcot to the BoardWalk is very do-able. You exit via the International Gateway between France and the UK and it's a 10 minute, very pleasant walk (or you can take the water taxi).
As for parking at the BW and walking to Epcot - that's a definite maybe. You'll get different answers. Again, we often do this (or a variation - the Beach Club is the closest hotel to Epcot), but I've been flamed on these boards for admitting so on the basis that only guests of the resort should park there. I have absolutely no qualms about doing it - we've spent literally tens of thousands of pounds at WDW over the years. And we only do it if we want to eat at one of the Epcot resorts, not just for the sake of it (we don't pay for parking at the parks anyway as we're AP holders so there would be little benefit).
If you drive to the BW and tell security at the parking lot barrier that you have come for a look around the BW, you will be let in (you will need photo ID) and given a 3 hour parking permit. You can do this at any Disney resort, but Disney advertises the BoardWalk as a destination in itself (along the lines of Downtown Disney), so no reason to feel guilty about taking up a space in the parking lot as Disney encourages you to do so. We often eat at the BW and then walk to Epcot, or vice versa.