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Display post grid on archive pages only available in pro version, Yes you can display post grid under any category or custom taxonomies like tags, or WooCommerce product category and etc.
you will need to manually edit the theme code. i can help you to integrate. please see the documentation
Ther is no trial version but free version available at wordpress.org https://wordpress.org/plugins/post-grid/ you can display post grid anywhere via shortcode, yes you can display also pages on the post grid.
Yes you can display ajax pagination on pro version, please see the demo
Let me know for more help.