Its been very long time to back in here to share the work around fixes. I have been configured public facing branding site in SharePoint 2013 multi tier environment.
Servers in the farm
SPAPP-V01
SPAPP-V02
SPWFE-V01
SPWFE-V02
SPSQL-AG (Availability group listener)
SPSQL-V01
SPSQL-V02
SPSQL-V03
Web application has been extended to Internet zone, which is exposed in public via F5, SSL configured on IIS.
AAM looks like
http://SPAPP-V01:8080 Default http://SPAPP-V01:8080
https://www.sathiya.io Internet https://www.sathiya.io
http://www.sathiya.io Internet https://www.sathiya.io
http://sathiya.io Internet https://www.sathiya.io
https://sathiya.io Internet https://www.sathiya.io
SharePoint search was configured with below topology;
SPAPP-V01 : Admin, Crawler, Content Processing, Analytics Processing & Index Partition
SPAPP-V02 : Admin, Crawler, Content Processing, Analytics Processing & Index Partition
SPWFE-V01 : Query Processing
SPWFE-V02 : Query Processing