Hi,
I would strongly recommend you to install the StyleMart with using QuickStart package. Installing StyleMart through pkg_stylemart is for "advanced" users (and for updating StyleMart). Because after install StyleMart through pkg_stylemart, none of the module will be generated, there will be no sample datas. You have to create modules, articles, menu items and build the Mega Menu manually.
OR at least, install the StyleMart through QuickStart to your localhost for TESTING and then check the published module, check their module positions, check the menu items, Mega Menu settings, articles etc.. then duplicate the same settings to your production site.
If you encounter any conflict problems; temporarily disable ALL the 3rd party extensions. There shouldn't be any 3rd party component/plugin that loads any jQuery Library. Because StyleMart is already loading jQuery which is enough for everything. (TIP: jQuery Easy plugin disable the all jQuery libraries -including StyleMart and your 3rd party plugins/component- and load only 1 jQuery library to website)
Regards.