A:AnswerFor the wifi extender see if you can set it up in "repeater" mode. This way the repeater and router will both broadcast the same SSID and password. Similar to an access point setup.
While this isn't exactly an answer to your question. It will allow the TV to connect to either.
Yet for how wifi actually works. It can not connect to "both" since only one device at your home is handling address assignments. Unless you are double NATed