Connected, no internet ad?

Ja
2

Have often times the message on my phone, that I'm indeed connected to the router, but I can't use the Internet (it is not on the router, other devices have Wi-Fi reception, laptop, other phones, etc.)

Si

Wi-Fi is not internet…

Wi-Fi is the connection between one of your devices and the router. But the router itself has to get internet.
So look, first, if you just have no Internet, but still on the router, which LEDs are lit / flashing / off.
If in general the DSL LED is off or slowly flashes, then your other devices usually have no Internet. Whether they are connected via Wi-Fi or not does not matter

ic

If that only happens on your phone, it has a bad wireless card