Safari Cant Find Server
The error message tells you what's wrong - Safari can't find the web page - so we need to focus there.


Changing your DNS to Google's DNS servers won't do anything as Google's (DNS) servers are completely unaware of your private network.
MySQL/SQL connections don't impact HTTP(S) connections - it's two completely different protocols used over two totally different ports.  If you did manage to "break" your database connection, Drupal would generate an error message and the site would break.  However, Safari would still be able to find it.
Because Mozilla and Chrome can both reach the website, it's not necessarily a firewall issue.  This tells you that the service is up and running and accepting connections.  You mentioned that you have it set for "allowing all incoming except for a certain app."  You could be blocking Safari.
Under the Firewall Options, it doesn't handle "all" the incoming connections, but only the connections for built-in software.  If you're using an AMP stack outside of what Apple provides, it's not handling it.  Disable the firewall completely to see if this is the case.


Now, the error message "can't find the server" is a naming issue not a connection issue.  If it were, say, the firewall blocking, you would get a "connection refused" message.  


ensure you're using the correct address.  Use the command line to be certain - `open -a Safari "apple.stackexchange.com"
flush your DNS cache - sudo killall -HUP mDNSResponder;
set your router as the primary DNS server (i.e 192.168.1.1 or whatever your router's IP is) as it will be be more familiar with your network
try http://localhost instead of the name - that will make sure it's going directly to your machine and not looking up anything.