I'm not sure why that would be for the torrent, but I have seen this happen before with VPNs.
What's happening is that your NIC is completely dedicating itself to that VPN network. That means, any network communication that happens with your computer is going to be handled by whatever network your VPNing into.
I don't know if this is a limitation of your VPN client or your VPN server, but one of the two does not support passing a connection out of that local network. This is actually a very intelligent way to do things - allowing internet connections while connected to a remote network could potentially open up a lot of security holes. The only way around this is going to be get a second NIC, or get a new VPN client/server.
The short answer is nothing is wrong - it's most likely a "feature" of your VPN.
For the torrents, try running a speedtest while downloading. It could be that your ISP is throttling you when they notice that your are downloading torrents.