under what law have these road systems been laid?
In Europe the implementation of bus lanes was officially sanctioned in the German highway code.
Bus lane
The first bus lanes in Europe were established in 1963 in the German city of Hamburg, when the tram system was closed and the former segrated tram tracks were converted for bus travel. Other large German cities soon followed, and the implementation of bus lanes was officially sanctioned in the German highway code in 1970. 
odd interstate routes run primarily north and south Yes, in U.S.  generally, most north-to-south highways are odd-numbered, with the lowest numbers in the east, and the highest in the west. how are the names assigned for it? The official route log published by AASHTO , has been named "United States Numbered Highways" since its initial publication. Within the route log, "U.S. Route" is used in the table of contents, while "United States Highway" appears as the heading for each route. is this system used in any other countries? Yes, in England, and South Korea,  to name a few. does it have a separate lane for heavy vehicles like buses? Yes, some countries incorporate bus lanes onto highways. have these lanes been effective? It is effective in easing traffic congestion. when were these lanes first laid? In 1940.
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Bus lane [SEP] History
The world's first designated bus lane was created in Chicago in 1940. The first bus lanes in Europe were established in 1963 in the German city of Hamburg, when the tram system was closed and the former segrated tram tracks were converted for bus travel. Other large German cities soon followed, and the implementation of bus lanes was officially sanctioned in the German highway code in 1970. Many experts from other countries (Japan among the first) studied the German example and implemented similar solutions. On 15 January 1964 the first bus lane in France was designated along the "quai du Louvre" in Paris and the first contraflow lane was established on the old "pont de l'Alma" on 15 June 1966.