Hi,
I can help you with the the z-index issue, because it is simple for me to resolve (but i just browsed your website and saw that you have disabled the module already), but i can't help you with the responsiveness. Because you are not using our template literally, this is something else, you have put some 3rd party modules which are not responsive-ready and used <table> which is the 10 years old web development techies, which has nothing to do with the "responsiveness", You should be using DIVs instead of TABLES. At the time while <table> HTML tags was being used, the word of "responsive" even wasn't exist.
You should better disable the "responsive" functionality from the backend. It is for your own good
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Also, you can't put everything together and expect all of them to work perfectly with each other. This is simply impossible. Even adding one single 3rd party module to your joomla will break the responsive layout (if the 3rd party module is not responsive and you don't know how to make it responsive). Providing support for 3rd party extension and support for your custom codes (in this case; <table>) is beyond our free support. I can't help you on this.
You should definitely disable the "Responsive" functionality from the "Template Configuration" section.
Regards