It seems to be based on perception. If I'm walking down a street, I can see a shop that is beyond the restaurant. Or I can see a shop that is past (ahead of) the restaurant.
But, if I'm looking directly at the shop, the restaurant is beside, or next to it. I hope this info helps to explain "beyond". Ha en Hyggelig dag!
No. While 'away' means away in any direction, 'past/beyond' implies a narrower scope of direction relative to your own viewpoint or course, or to the perceived front of something. 'Bortenfor' covers that same scope.
"Farther away than the restaurant" technically works, but both 'past' and 'beyond' are more elegant ways of expressing it.
The expression is 'past the restaurant', not 'passed', and it's an error a lot of native English speakers make. Compare:
"I was out walking when I passed a restaurant"
"The bookshop is just past the restaurant on the right"
This blog gives more detail: https://blog.oxforddictionaries.com/2015/01/07/passed-past/