what are the implications of running a FQDN as internal AD domain and point A-record for website to different host?
This won't work. Domain Controllers register A records for the AD DS Domain that they are authoritative for. This is why domain naming is so important.
So if your DCs are 10.1.1.1 and 10.1.1.2 and your domain is company.com, the internal AD-integrated company.com zone will have A records at the apex of the zone for 10.1.1.1 and 10.1.1.2.
As an aside, you should be concerned that IIS in installed on your DCs. That's generally not good.