Cross-Device Viewing/Gaming

[PedroSpecialK]

Starting a catch-all topic for this, as I imagine I'm not the only one who's technological savviness has gone by the wayside in recent years. Here's my situation specifically:

Living Room: Big TV, XBox One
My Room: Soon to buy a 32" TV

I'm trying to figure out what I'd need to buy be able to:

1. Stream movies/Netflix/Amazon video (via Google Cast) etc
2. Mirror my XBox One's display from the HDMI port on the big TV to the TV in my room.

I'm less sure on 2 - my idea was to get an HDMI splitter and use a wireless transmission but I have no idea if that's even feasible. I'll be using my controller from my room to play online games, so even though it's only ~25' away I'm assuming there will be some lag.

Has anyone tried something similar to #2? I'm not ruling out buying another XBox One for my room specifically, but that'd be a last resort... the router is in the living room, and a wired connection is the only way to go for online FIFA.