A strong edge-colouring of a graph G is a proper edge-colouring such that every path of three edges uses three distinct colours. An induced matching of a graph G is a subset I of edges of G such that the graph induced by the endpoints of I is a matching. In this paper, we prove the NP-completeness of strong 4, 5 and 6-edge-colouring and maximum induced matching in the case of some restricted subclasses of subcubic planar graphs. We also obtain a tight upper bound for the minimum number of colours in a strong edge-colouring of outerplanar graphs as a function of the maximum degree.