Well, the select all feature might not be possible to deselcted without making direct modifications to the core code I’m afraid.
The others however can be resolved. Because you have an elementor products widget, it needs to be triggered to reload on the page load event. Instead of that code, use this one to get the page URLs:
var id=1;
ASP.api(id, 'getStateURL')+'&asp_s=&asp_id='+id;This will generate the URLs with a trigger, so once the page is loaded it will force an empty search to refresh the products list on the Elementor Products widget to display the correct ones.