Take a look at Kodi, this may be exactly what you're looking for
Linux
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Thanks, will take a look!
Its also got a companion remote app for mobile devices so you may not need the air mouse
Only problem I see with this, is that at least Netflix limits you to 720p when using linux. I imagine Amazon and Disney might also have similar DRM related restrictions. Other than that, everything on your list should be doable.
That could be an issue, though given that the TV the system uses is almost as old as the laptop and is 1080p, that becomes less prominent)
You could use this as the DE https://plasma-bigscreen.org/get/ https://packages.debian.org/stable/kde/plasma-bigscreen
Chromium has the ability to install webpages as apps.
A plymouth screen can be used to cover the scary boot messages https://askubuntu.com/questions/2007/how-do-i-change-the-plymouth-bootscreen
Seems like a list for bed time reading ) Thanks!