Do you want to achieve this visualization in an ArcMap Desktop application or a web map?
In ArcGIS you can put these different categories of roads on separate layers. In the Layer Properties you can set that a layer only displays at certain scales. So you can adjust your layer with the smaller one line roads to not display above a certain zoom (out) level.
See an instruction here at the ArcGIS Resource Center
To get the two line symbology you need to double-click you line symbol in your table of contents in ArcMap. On the left you can then choose a preset symbol if you have some symbology libraries installed (ESRI has some standard symbols for highways that might fit your needs) or you click to edit the symbol on the right side of the window. There you can create symbols that have more than one layer which is what you need in your case. Think of your road symbol not as two lines but as three lines on top of each other: a thick black line with a slightly thinner green linie on top with a thin black line on top.
You can find help on creating symbols here in the ArcGIS Resource Center
For the symbology of two lines with different colours next to each other you need to have a symbol with two layers and give one line the type "Cartographic Line Symbol". Then you can specify an offset for that line.