I’ve used an Acer Spin 5 and Dell Latitude 7440 with Kubuntu, Ubuntu, Arch, Fedora and NixOS over the years without many issues.

I’ve heard that the x360 laptop you have may be a little troublesome but you can always test things out on a live Linux USB.

• I’ve heard that the sound quality might be degraded on Linux, or certain speakers don’t work
• The flip switch doesn’t work, meaning that the keyboard and trackpad aren’t disabled when flipped.

Ofc, there are a few x360 laptops so it might not apply, I’d encourage you to just give it a go with a live USB.

For using your stylus for note taking, I’d recommend trying Xournal++ and/or Rnote

Not recommending against RustDesk - it is a very cool project - but regarding the “Why?”, you could use a VPN or something like Tailscale which has MagicDNS that’ll resolve hostnames of computers to their local IP address. You can use this with GNOME’s RDP server to remote in from another device pretty easily.