A:Answer you CAN watch a streaming program while recording something over the air.
You can also watch an over the air channel while recording a different over the air channel. In fact, it's a 4-tuner device, so you can record multiple programs simultaneously.
BUT, this product is the OTA (Over The Air) model, meant primarily for viewing locally broadcast signals brought in by an external HD antenna. The unit has an internet connection, but only to allow watching internet streaming channels like Netflix, Hulu, Amazon Video, etc. It can't decode "cable TV", like the Syfy Channel, History Channel, Turner Classic Movies, things like that. You need a different Tivo for those.