[Zubersoft]

WiFi is generally more stable but this does depend on the stability of the network you connect to. As far as your question, you would want to connect everything to the same network, so if everything is connected to your modem (which is acting as the router), then that should work just fine. You can use a phone as a WiFi hotspot if you encounter problems with the modem though. A different IP address should always be assigned by your router using DHCP, so that's generally not something you need to worry about. Most routers try to keep the IP address assignments stable, but if you are finding that the IP addresses switch a lot and this is a problem for you, you can use DHCP reservations in the router settings to ensure your devices always get assigned the same IP addresses. You don't have to keep the IP addresses the same to use the WiFi connection though - that is not a requirement. 

Mike