Not necessary. TV remotes use so little power the batteries can last ages if you just switch their positions once every while. Mine has been using the same set of batteries for 14 years now.
Not anymore, they have always on microphones and motion leds.
And bluetooth.
Even for those dumb, infrared only remotes manufactured these days, I find they use an unreasonable amount of electricity. The batteries I put in it usually die every year. I’m not sure if the design and materials in the remotes became worse, or the batteries are.
Ah, I never got a ‘smart’ tv because they one I have still works well and I don’t need my tv spying on me to sell ads. So I never had those.