How to update the search title and page title depending on facet options
The solution is on the Facet API Bonus module's project page:

Integration with Page Title module Now you can set search (views) page titles using Page Title module. Module provides possibility to set tokens 'facetapi_results' and 'facetapi_active' groups. So in title we can display number of results on the page or values of active facets. As there can be multiple active facet values please use following pattern to use facetapi_active tokens:
list&lt;[facetapi_active:facet-label]: [facetapi_active:active-value]>

This will make coma separated list of active facet labels and their values.