Your city relies on the rest of the world to trade its resources and other things. That is why buildings in SimCity Social need to be connected to the interstate (interchange at the bottom of the map) to be functional. Decorations and Landmarks don't need road to be functional. Roads are free, do not require Energy, and are always at your disposal.
If you build a road over a river, the road will become a bridge. Bridges cannot bend, intersect with other bridges and intersect with normal road. You also can't build two bridges right next to each other (think of it as a 4-lane avenue).
Another special situation for the road is that you can cross roads over railroad tracks. Simply draw a perpendicular line over the railroad, and the railroad crossing will be created.
You might have noticed you can't draw a road straight over the railroad. And it's not a bug, SimCity Social is not a game where you can build a tram. However, you can build a tram road. You just have to place every piece of road one by one. You'll notice your Sims just drive with their cars over it just as a normal road. You can even place your emergency services next to it. Disadvantage is that it's not suitable for cosmetic purposes.
If you wish to get rid of a road you built, you can use the Bulldoze button. Just click it and then click the part of road you want to remove or clearing out bridge.