Does your router indicate that you have DS-Light? I think O2 provides each customer DS-Light until they ask for a real IPv4.
To your second question: In case of DS-Light you don't need a new IPv4 IP every 24h because your IP is not public facing.
PS: I don't be sure, but the Fritz Remote Apps use IPv6 to ensure that they also work with DS-Light.
Does your router indicate that you have DS-Light? I think O2 provides each customer DS-Light until they ask for a real IPv4.
To your second question: In case of DS-Light you don't need a new IPv4 IP every 24h because your IP is not public facing.
PS: I don't be sure, but the Fritz Remote Apps use IPv6 to ensure that they also work with DS-Light.