the new upc tv box need the connection to the connect box or you can use it without this connection and only with the wall socket ?
Connection to the wall socket for live TV.
Connection to the internet (the Connectbox in your case) is needed for Replay, Recording, even pausing live TV. Maybe even the guide - don't know about that.
Basically, there's no storage in the new box so everything not live is taken from UPC's servers/cloud, which requires internet.