Minor Houzez wordpress theme customisation

Hi,
I'm using Houzez theme and need someone to help with 2 minor customisation work

fix the empty search returning all posts issue. Empty search must not return anything, and ideally display "Search criteria required" The fix must work for:
-advanced-search
-splash-search
-agency-search
-agent-search

The fix must be carried out in my child theme to ensue it survives future upgrade.

Show me How I can preselect an entry in a drop down field (Status) when a page is accessed using is_page function. I want to create two pages, "For sale" and "To rent". Status field selected as "For sale" when page is selected and "To rent" status selected when "To rent" page is selected.

see https://www.zoopla.co.uk/to-rent/ and https://www.zoopla.co.uk/for-sale/