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.

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. If you do implement an Access Point DO NOT implement a DHCP server - use the server on your router - thus all devices should be on the same network segment.

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.