An Access Point is NOT a router. See Using the Raspberry Pi as an access point to share an internet connection (bridge) in Access Point
Adding an Access Point to an existing network just adds complication, and a normal network does not need one.
You can host on the Pi. See https://raspberrypi.stackexchange.com/a/90864/8697 for links to tutorials. I use nginx to host on my Pi, accessible by hostname.local.
Raspbian by default implements Zero-conf. Whether other devices on your network support this is not a Pi issue.
I suggest you implement whatever you plan to do in stages.