The answers to your questions, as best as I can:
1) Choking is something that happens when a client no longer will send (or recieve) any further data on a particular connection. Local can choke remote, or the remote can choke you (local). The random is something Tixati seems to do when the connection is first setup and it is deciding how it should handle the data on the connection. I usually see random when I'm seeding, as the local doesn't really need any data from the remote (not file data anyway).
2) Sounds like a good idea to me, especially if their connection has issues again.
3) The control reply during the UPnP "process" would be when Tixati requests that your router start port forwarding on whatever port you have Tixati set at (basically). This error sounds like an issue with your router, although it may also be due to something like that port already being forwarded to somewhere else by a different application. I would first check that and then try some other approaches. You can also disable UPnP and just manually forward the port on your router. If you like, feel free to post the logs that Tixati spits out onto the home page about UPnP if you can't figure it out.
And if you feel like reading more about UPnP for some reason, check out http://www.upnp-hacks.org/upnp.html