Basically- if I have a VPN running on my computer but my phone is just on the regular network, does it slow the network down significantly on the phone?
No. But the network traffic that you put through the VPN (streaming, torrents, game update downloads, etc.) will still impact your local network just as they would without the VPN.
Not specifically. A VPN itself adds pretty much negligible load on the network.
But … people do tend to imagine VPNs like magical internet portals where the rules don’t apply. And so they tend to do rude shit like torrenting 300 GB files off them like casual.