First of all I applied “medium privacy more compatibility” scheme in HMWP settings. And in your site’s htaccess file I’ve added the lines within –
# HMWP
.
.
.
# EOF HMWP
Actually these lines should be auto added by HMWP after line “RewriteRule ^index\.php$ – [L]“, but in case of your site’s htaccess there was already lots of stuff added into htaccess by different plugins and hence the confusion.
The search is also working now. I unchecked “Search base redirect” option in Permalinks & URLs tab.