any european city in particular where this can be seen?
Yes, London.
Bus lane
On 26 February 1968 the first bus lane in London was put into service on Vauxhall Bridge. The first contraflow bus lane in the UK was introduced in King's Road, Reading as a temporary measure when the road was made one-way (eastwards to Cemetery Junction) on 16 June 1968. The initial reason was to save the expense of rerouting the trolleybus, which was due to be scrapped on 3 November of that year. However the experiment proved so successful that it was made permanent for use by motor buses.
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. under what law have these road systems been laid? In Europe the implementation of bus lanes was officially sanctioned in the German highway code.
wiki:12579488
Bus lane [SEP] History
On 26 February 1968 the first bus lane in London was put into service on Vauxhall Bridge. The first contraflow bus lane in the UK was introduced in King's Road, Reading as a temporary measure when the road was made one-way (eastwards to Cemetery Junction) on 16 June 1968. The initial reason was to save the expense of rerouting the trolleybus, which was due to be scrapped on 3 November of that year. However the experiment proved so successful that it was made permanent for use by motor buses.