This would be dependent on the setup. If you need internet connection, then the wireless access point has to be connected to the router else it is not required. We understand two scenarios where this is implemented.
Wifi with internet connection
Let us assume that you have a wifi router with internet connection at home. The internet connection has to be extended to another room. For this you are planning to use a wireless access point.
In this setup, the wireless access point has to be connected to the internet router. This can be done using cable or wifi. The wireless access point works in access point mode when it is connected using the cable and in repeater mode when wifi is used for connectivity.
Wifi without internet connection
Assume that you have internet connection at home. You also need wifi at a specific room, but internet is not needed. This could be a scenario where you are setting up a private wifi area in your house.
In this case you need not connect the wireless access point to the wifi router. The wireless access point can be configured independently and all users in the private wifi can connect to it.
1. What should be the IP address of the access point in scenario 2 where the wifi router is not used
The IP address should in the same range which is configured on the wifi router. For example, if the IP range is 192.168.0.1-192.168.0.254, the IP address 192.168.0.100 can be configured for the access point provided it is not configured for any other device on the network.
2. What should be the IP address of the access point in scenario 2 when the wifi router is not used
In scenario 2, the wireless access point is not connected to the wifi router. So any IP address can be configured on it , since there is no physical connectivity between the networks.
Check out our pick for the Best wireless access point for home.