You need a router or a proxy. A proxy would be annoying, so a router is preferred.
If you don’t have control of your edge router, just get a cheap Pi-type device, install OpenWRT, setup your VPN connections, then create a route on your network to point at this new device for whatever you need it for.
If you simply want to use it at-will for certain things, you can put a proxy on it.
As to your other issues, it sounds like your WG connection is just dropping, in which case it won’t automatically reconnect by default. OpenWRT has plugins that can monitor that and reconnect when it drops, or you can script it pretty quickly as well.
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The default gateway for the new device needs to be your existing router in order to get to the internet. Then when you create a new WG connection, you ensure all traffic that gets passed to this new device forwards through the Wire guard tunnel.
PC > WG-router > existing-router > internet
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Pretty much got it. Any other static routes you setup will be static to the new router only, but otherwise that’s pretty much it. Devices with static IPs don’t participate in DHCP, so it won’t cause a conflict. Just make sure DHCP is disabled on the new device.
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You will need to set up IP masquerading.
Why not route traffic through the VPN via your router? Should be pretty easy with Mikrotik
If you can run WireGuard on all your devices, you may wanna set up a multihop node that forward outbound traffic to the VPN tunnel via that hub
