Hey there! Glad you are finding Stones and Rivers cool!
T
o answer your questions
The main reason for the Asymmetrical board is for each player to feel like they had "their" side (which worked well in playtests) but I see no reason why you couldn't use a Go Board as a wood board at home!
Stones are able to push any piece 1 space into an open space. If a stone is moving up it can push up, if it is moving down it can push down, same for left and right.
Rivers can be moved by other rivers as well but there is only one push a turn.
Hope this helps!