1 and 2.: Yes, it's actually a bug in WooCommerce, where the Visibility and one other taxonomy (I can't remember) is called 'Tags' instead of their proper name.
The product tags are the 'Product tags', the other two is not neccessary to include.
3. I'm planning to add a complete uninstall & deactivate feature, but it's not working yet as I want it to. For now, to completely uninstall the plugin, first de-activate then delete it, then also:
– Delete the wp_asp_index, wp_ajaxsearchpro, wp_ajaxsearchpro_priorities, wp_ajaxsearchpro_statistics tables in your database
– Delete any option in the wp_options database table starting with the 'asp_' prefix, there should be only a few, namely: asp_version, asp_updates_lc, asp_updates, asp_media_query, asp_st_override, asp_compatibility, asp_performance_stats, asp_recently_updated, asp_glob, asp_recreate_index, asp_woo_override
– Delete the wp-content/uploads/asp_upload folder
And that's it, I believe this is all the information stored by the plugin.
If you like my products, don't forget to rate them on codecanyon :)