Bug 2 - Yeah, that's bothered me for a while as well.  The actual functionality of the expanded borders is there, but you can't see it graphically represented.  You can force it to update by choosing to build on a resource node if there is one (you can then cancel it and the graphical update is still applied).  I haven't found any other workaround, although it's only a workaround if you know that the borders have expanded.

Bug 3 - I've used Lower Land successfully in the beta so far.  AI player had his town blocking the only path between a lake and a mountain, so I carved a path through the mountain.  I used it only once on each of 6 tiles and walked through, no problems.  

In you third screenshot, it looks like you're walking through the path you carved.  Where did you encounter the problem?  Have you looked it it from a more top-down perspective?

And once you've turned on the grid, if you go into the cloth map, it's really easy to see what's been affected.

Remember that Lower Land only works on one tile at a tile.  You cast it on the tile you want to become traversable.  If you are trying to get through a mountain 3 tiles wide, you have to cast it 3 times, once on each tile.

Also, like mmilleder said, you're not going to get a new road.  That's just not something that's supposed to happen.