The designer Alban Viard has asked me to answer your questions. These clarifications can be considered official.
- Do you get the bonus point to connect to any network across an edge, so also your own network?
The bonus applies ONLY to cubes of the same color. Each time you add a cube to a network, the value of the network is increased by one if there is also a same-colored adjacent cube on the other side of the map.
In this example, the light blue network has made one edge connection (hex 55/56), so its value is increased by one.
If the two cubes in the lower portion of the map had instead been placed one hex northeast of their current location, then there would be two edge connections (hex 55/56 and now also hex 53/54) and the value would be increased by two instead of one.
- When you cross over an edge, the new cube will be adjacent to the cube (and thus network) you started from at the other side of the edge, so does a railroad get a point every time it crosses an edge?
Yes, if you are directly crossing from one edge to the other, then you would always get the bonus for having adjacent cubes on each side of the map.
- Do you get points for building along an edge? So if I build to an edge hex which is connected to a network on the other side, the railroad gets a point. If I now build on an adjacent hex on the same side of the edge which is also adjacent to that network on the other side, does the railroad get another point?
Yes. But each edge hex is adjacent to one and only one hex on the other side of the map. So if you build in this way, you will have to eventually place two cubes for every extra point you are getting.
- In other words, will everybody be hugging the edges like crazy in this game?
That is for you to discover!