How can I show parent and child terms in facet search filter block for a taxonomy field having simple hierarchial select as widget type
I'm presuming you are using FacetAPI and Search API Solr.

You need to add some settings to the facet itself at Search API > Index > Facets > [Taxonomy name]:
http://example.com/admin/config/search/facetapi/[indexname]/block/field_[taxonomyname]/edit

You'll need to 


Expand the hierarchy
Treat parent items as individual facet items
Don't flatten hierarchy
and minimum count zero (ie: show even when empty)