Does your TV support a wireless connection to it as a second screen. Check if your PC can find it with WindowsKey/p and "Connect to a wireless display". Not sure how widespread that feature is, but I know my 2015 Samsung TV supports it.
Don't believe that's a thing. What browser are you using?
parsec, steam link
The Windows function you're trying to use, despite using the word "Cast" is not using the Google Cast protocol. It uses Miracast, which is the standard Microsoft backed and which a lot of TVs have built in, but is not directly compatible with Google Cast. There's nothing that'll cover you here, other than going straight to your TV which is showing up in the list.
if you want to cast content from the browser - for the most part that is chrome cast,
if you trying to cast a video file from your PC - you can do that via VLC
Games - steamlink, nvidia now
Photos - windows built in photo gallery should be able too
The problem with parcsec and any other app based option is that apps are currently limited to 1080p, so it looks crap on a 4k screen.
VlC?
HDMI cable