What!? You can (should) assign IP addresses outside the range of the DHCP pool. There is no reason why the AP can have all it's interfaces configured by the DHCP server on the router, using the same 192.168.x.2 address you are using now. On the other hand, on the AP only the LAN interface needs an IP address (and just for maintenance tasks), the IOP and GUEST could be configured as "option proto 'none'", and everything will work.
Yes, the DHCP server on the router announces the router as the gateway; otherwise, clients could only reach other devices on the same network segment.
Yes, but that information is only needed for the AP itself to reach the internet, no other device (even wireless clients connected to the AP) requires that info.