Hi,
1) please read my post above, I have written about the "Phoca Facebook comments" module not about K2. This means, Phoca Facebook module is a module like any other module in Joomla! and this means if you have some specific program like K2, you can manage Phoca Facebook module like any other module.
2) Yes, I don't know K2, this is why I have answered like I answered (short version). Now long version: I don't know K2 but the Phoca Facebook module is standard Joomla! module, I don't know how K2 manages the modules but I know that the Phoca Facebook module is a module like any other module in Joomla! So if you are using K2, you will probably know how K2 manages the modules in Joomla! so the same way like K2 manages all other modules the same way it will manage Phoca Facebook comments module.
So if this is the question: "How to stop Phoca Facebook comments to appear in K2 category listing."
I can answer it: the same way like K2 can do it with any other Joomla! module. I am sorry, but I don't know any other better answer. For better answer you need to visit K2 forum and ask how to stop displaying some module in K2 category listing as it seems K2 category listing is rendered by K2 and it seems there is some feature to render some (maybe selected, maybe not) modules.
But as I wrote, I think, this is more a question on K2, regarding K2 my experiences is zero

From your post above, I think, maybe you didn't understand my answer correctly but maybe I didn't understand your question correctly, so if yes, sorry for this.
BTW:
After six days
I don't know how phpBB does count the days but the question was set on 11 aug and was answered on 15 - this are not six days
... Please, you didn't pay me for anything, so I don't have any obligation to answer you immediately. But please do not take this like rude answer. Of course I would like to answer the question immediately but I do my extensions in my free time and if there is a little bit time I am trying to answer questions - of course in my free time - it is really hard to find time to manage all the extensions, all the documentation, all the translations, fighting spam and ddos attacks, all the support in free time, etc. So if you are using some of my free extension and you get some of free answer (even it can be confused because of misunderstanding), please be patient, I am trying to answer all the questions - but it takes time as first I need to do my regular work like others. Thank you very much for understanding.
Thank you, Jan