The council could have co-opted additional members in the 35 days following the 2015 election, to make up the shortfall in nominated candidates. After 35 days, the district council can make appointments, although it may feel that it has other matters to attend to, and not bother. If a vacancy arises, for example by resignation, then all the vacancies must be publicised with citizens having the option to call for a poll (although at the parish council's expense).
You could try to get the district council to insist on the parish council making appointments, or ask the district council to make appointments itself.
So far as I know, there are no particular rules that have to be followed when a council decides who to co-opt. It's good practice for all submissions from candidates to be made public and for the council to decide on the basis of the published submissions, so as to make the process as open as possible. But that is not obligatory, and I don't think there are any specific grounds that can or cannot be used in the decision making. (Co-option is always a very second rate way to appoint councillors - unfortunately, it is too costly to have a poll every time a vacancy arises).