Does the device need to be re-added after changing the router?

If your router's name and password change, you need to reset the device and add it again.

Further questions:

How to add device in App for Internet connection？

https://fchelp.cloud.alipay.com/helpDetail.htm?tntInstId=Dss_sP5T&helpId=89486300&helpCode=SCE_00000163

What if the device is offline

https://fchelp.cloud.alipay.com/helpDetail.htm?tntInstId=Dss_sP5T&helpId=89434595&helpCode=SCE_00000163