Just a simple question. I want to change all my light switches with zigbee switches. But is it possible to use those light switches when the internet (,wifi) is not available like due a maintenance or something?
Zigbee has nothing to do with Wi-Fi, so it will not be affected by the availability of your access point.
Except when you use cloud services and your internet is down, you cannot control these devices anymore.
If your local network is down, you might not be able to control your HA anymore but if these lights are in an automation, those will still work.
If you have mains powered single-gang light switches (ie only one switch), they should continue to work manually even when HA (including Zigbee) is down. If you have two- or three-gang mains powered switches (ie two or three switches), they will not.
Only buy one to start with! See if it performs as expected.