To give an idea of distances, the entire walkway that goes around WS in Epcot is 1 mile long. So, by my estimate, to walk from BCV thru the International Gateway, past the UK and Canada to get to WS and then out to the monorail would probably be close to 1 mile.
If you are using the monorail to get to MK, you would need to switch monorails at the TTC. Once you get to MK, there is a very steep ramp to get from monorail station level (about 2nd floor hright) to ground level. You would probably be better off riding the bus to MK. When DH and I stayed at YC over New Years, we found the bus to MK to be convenient and hardly anyone was on it. YC shares a bus with BC (or at least did then). The BC stop was pretty close to the BCVs.
For renting a manual (push) wheelchair or
scooter (
ecv), these are the places that DIS posters have used and recommend:
Care Medical:
http://www.caremedicalequipment.com/
Walker Mobility:
1-888-726-6837
www.walkermobility.com
RANDY'S Mobility is in Kissimmee 407-892-4777
http://randysmobility.com/
Colonial Medical
http://www.colonialmed.com/about_cms.html
They will rent
ecvs to anyone over 18, but none of them rent power wheelchairs unless you are already an experienced power wheelchair user.
You can request a wheelchair from the resort as was mentioned, but even if you plan to do that, I would still take the contact info for these places along. Some people have posted that the wheelchair that was available (they are first come, first serve) was an extra large when they needed a narrow one (or vise versa).
For navigating Epcot, there is a large hill between the UK and France. It's a little better (IMHO) to come from France to the UK rather than going from UK to France. Other than that (and the walkway to the International Walkway that was mentioned), WS is pretty flat. There are wicked hills to get up the Land Pavilion and to get up to the Wonders of Life.