Traveling between Spain & Portugal

I would like to get to the ne corner of Portugal (Bragança area) from
Madrid. It's easy enough to get to Zamora or Puebla de Sanabria by bus
or train. In fact, Pueblo de Sanabria is probably about 15 miles away,
a walkable distance for a person like me who likes to walk on
vacation. So my questions a
1) Is there public transport between either Zamora or Puebla de
Sanabria to Brangança? And 2) If I walk from Puebla de Sanabria to the
Portuguse border, can I just walk across? I don't see why I couldn't,
but walking isn't exactly considered to be the most conventional mode
of transportation. Thanks.