Yes… Each .torrent file is assigned with a personal passkey that is unique to each user's account. This is how the system tells what user is seeding what, based on the announce URL that the torrent client uses for that torrent. If you are leaving multiple computers running across the same network using the same public facing IP address, it is critically important that both torrent clients are configured to use different ports, and that the router that you're using for your connection has the port your torrent client uses forwarded to those devices both in TCP and in UDP. This will ensure that you are able to get proper incoming connections.
As for your question about ratio, I will put it simply. No matter what device or connection you are using, any data that is transferred DOES count towards your ratio. Just be aware though that a torrent client will only update with the tracker once every 30 minutes, and as such, you may notice a delay in the overall stat totals updating. This is normal, and the stats do eventually update, as long as you do not close your torrent client, or reboot your computer.