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Yes, as this is an internal problem, you will be charged.
Are you having similar issues with any other devices in your property?
Extenders "may" be an issue for the Internet channels and catch facilities (e.g. Iplayer, Netflix etc.).
They WON'T be the cause of Freeview issues though ... that may well be that the aerial signal isn't strong enough. (Remember that the Youview box - if it is YV+ - has 2 tuners in it; one for watching and one for recording. Your TV will just have a single tuner).
I'd be happy to see if I can help you. If you Private Message me your phone number or account number we can discuss your set up and how we can get your service working for you.