Can you access the XAMPP computer from the LAN using the IP address of the XAMPP computer just using http:// ?
You can't access the computer that XAMPP is installed on from another computer on the lan using http://localhost
as it is a local loopback address 127.0.0.1
However from a LAN PC you should be able to access using the IP address of the XAMPP computer providing you add the details to the HOSTS file of the LAN PC or use a setting in your LAN settings (DHCP/DNS perhaps) or router to redirect (not sure which as I don't have a LAN).
The certificate error is normal for a self signed server certificate which is how XAMPP is configured for localhost.
Apache is configured in the \apache\conf\extra\httpd-ssl.conf to listen on port 443 for any connection - local, WAN or LAN.
Make sure that your router or firewalls allows access to all the ports Apache and MySQL require.
A full list can be found here:http://www.apachefriends.org/en/faq-xam ... html#xpsp2