Ahhh.. much easier to see the code on the page now. Notes:
1) Mootools isn't being loaded twice, it's 2 different parts of Mootools (Mootools Core and Mootools More). That's common on J2.5 sites. I don't know what's enabling them, and I'd just say to ignore it for now as an issue to investigate.
2) JQuery is being loaded twice.. once by K2, once by the Chat module. I would recommend *trying* to:
a) Re-order the JChat system plugin to be a lower number / before the K2 system plugin
b) Go into the K2 admin area, click parameters or options and set it to not load jQuery in the front-end
That, again, likely won't fix the issue.. but one less inclusion of jQuery is a good thing.
As for the JChat issue, when I try to create a post in the "Group Chat", nothing appears. When I reload the page, it does appear. I'm assuming that's what you mean you say "glitchy", but still not sure.
I don't see the exact cause of the problem, but when I submit, the following Javascript error appears in the console:
Uncaught TypeError: Cannot read property 'status' of undefined main.js:384
(anonymous function) main.js:384
c jquery.js:3
p.fireWith jquery.js:3
k jquery.js:5
r
The main.js file is from JChat. They may be able to help diagnose that further (or know of issues/conflicts with Facebook integration). It wouldn't hurt to pass the question by them to see if they know what's going on with that error message, at least.
One thing you can try in JFBConnect is to enable the "Include jQuery / Bootstrap" setting in our configuration area. It will load a very specific jQuery compatibility layer that should make JFBConnect less visible to other Javascript heavy extensions. It's worth a shot at least.
I hope that helps make some progress.. bug again, please confirm if the issue with the JChat box is what you're actually seeing or not.
Thanks,
Alex