The Track-It! Remote product relies very heavily on your network environment. Because of this, some customers find that it installs pretty easily with minimum intervention, while others find that there's quite a battle needed to get it to install.
Once installed, there typically isn't much that you have to do to keep it working, and to use it.
Because each environment is different, what we normally do is focus on a single machine, and keep good notes on what's required to make it work. We then take those corrective actions on another machine, and see if there's any additional configuration required. After maybe 3 machines, we have a good feel for what will be required, and then you can use a GPO or something similar to get everything set so that you'll have a high success rate on a mass install. (You can always use that same GPO to undo everything after the install process is completed.)
This environmental dependency also makes any serious troubleshooting a bit complex. In your description, you give several symptoms, and each has numerous possible causes. For example, the "name not found" is a generic message that simply indicates that your Guest cannot communicate with the specified Host over port 6502. This could mean that the Host isn't installed or isn't running on the target machine; or that the Guest can't access port 6502; there could be a DNS issue preventing resolution of that machine's IP; or the machine may simply be turned off. There are a few other possibilities as well, though they tend to be less common.
I'd really encourage you to call our support line to work through these, but bear in mind that with the wide range of symptoms you're seeing, we're probably going to need to break this up into more than one session. If I were working with you on it, I'd start by focusing on a single Guest machine, and figure out what's going on there; then I'd give you "homework" to make the necessary changes so that you can get all of the Guests installed and functional. Once we reached that point, we'd shift over and focus on a couple of Host machines. Of course, each tech may take a different approach, but we can get you resolved....it'll just take some time because of your range of symptoms.
Also, it would make troubleshooting a lot more streamlined if you could have the Telnet Client installed on the Track-It! Server, and on at least one or two Tech Client machines. You can remove it when we're done, if you don't like having it installed.