A:AnswerYes I had the same problem about the same time frame. Changed the batteries also. I had to unplug the device and waited two minutes and plugged it back in and it works again. If you didn't try this already I would try. I think it's the device not the remote.
A:Answercat 5e, 6, 6e all support 1 gigabit at 100m. any of them will work fine for your shield. if you're outfitting your entire house with ethernet go with what will future proof you and you can afford.
the most important aspect if you're running cabling of significant distance within your home is to make sure to always buy 100% pure copper ethernet cable. stay away from copper clad / copper plated etc.
A:AnswerThe shield will come with its own power adapter, but you will need your own HDMI cable to connect it to your TV reliably. It does not come with the HDMI cable.
A:AnswerEverything depends how old you need to be more specific do you mean that you don't have hdmi? If so you can get an adapter rca converter to hdmi so from tv to the adapter and from the adapter to the shield better if you have a home theater.
A:AnswerThat depends entirely upon the software you install. If you have a streaming service like Hulu or Fubo or YoutubeTV that has your local channels then yes. But it doesn't not just have random tv channels available.