1) What element do you use to display products there? It’s not the default WooCommerce shop page.
2) If you installed the third-party plugin than you need to replace theme header search by the plugin search by additional customization of the header. If you need help with additional customization submit customization request here.
1) That page is the simple page that you created from Pages > Add new, right? Did you use WPBakery Products element or WooCommerce shortcode to display products there? Provide me temporary Dashboard access to your site to check because I can’t get a clear answer from you and it slows down the support process.
2) There is no “search by tag” option in our theme. If you want to implement this you need to find the third-party plugin that includes this option, set it up according to plugin documentation. After that disable theme default search form from Theme Options > Header > Header layout. Copy file with the header structure that you use to child theme and edit it to add search code (xstore/headers/xstore.php) http://prntscr.com/nf7kww
or don’t change the header code but copy etheme_search_form function to child theme (xstore/framework/theme-functions.php) and edit it according to your needs.
What code to add depends on the search plugin that you’ll choose. Contact plugin developer for detailed instructions about search code.