If I may, in reading this thread. I can only assume why the question of if the templates have been removed was asked because no further discussion about it has yet been provided.
Unfortunately and self-stated your lost in how all this works and what to do. At the same time all of the specific actions that were taken to get to this point have not been outlined. Yes, identifying all of them will take time and those helping if they choose to would have to expend what could be a lot of time and energy, so going through them all may not be as valuable as understanding why what has happened has happened.
During the install of the first templates, they went well, no problem. Sometime after that, the templates installed caused problem. My assumption regarding the questioning of the removal is that the thoughts of those asking is that if the removal was performed incorrectly/incompletely, then that process caused the problem(s) seen later on. By the statements that not sure about sql packages and the other things, well if there was additional software/instruction to be used that it isn't/wasn't known, then there is the probability that something was done wrong. Again latching onto both parts of a potential incorrect removal of the earlier templates or incorrect install of the "newer" templates. Generally speaking any number of templates can be installed on a system. The fact as lat9 pointed out that a file is not a part of a standard install and the referenced database table also is not typical indicates that the template package that includes that specific file is the one that was not installed correctly. It does not mean that there are no other errors, but for starters if the template that has that file set is properly installed then at least that error will go away. On the flip side as also suggested if that particular template is fully removed then the problem will go away. Removal is not just about taking files off the server as discussed. Some files have instructions (typically including the word(s) insert, update, or delete) associated with changing the database. As a result, the database may already have been changed by one or more of the template installations.
As for file overwrites, it is important to always know what file(s) are being overwritten and what the overwrite will do/change. Sometimes a notification is given that a folder is being overwritten, but this may just be an indication that the same folder name exists and that there is no real change to the folder, but the files inside that folder, that's a different thing.
Well written programs, plugins, and the like will come with some form of instruction to install and even better to remove the changes made. If you have already sought one-on-one assistance, then maybe the above will help you in the future, but if you do a little bit of comparisons of what you were trying to install with what is reported and possibly take a moment to review the install instructions for each of the items tried then you will be able to solve the problem. Otherwise, the various ways to obtain further assistance have been outlined above.
Just want to further state that at no time did anyone say you should remove the earlier templates, they asked questions to gain an understanding of what actions were taken and is one of the reasons that the posting guidelines suggest providing as much information as possible so that direct assistance can be provided with minimal questioning back and forth. Hope that helps.