Hello,
Thank you for your report.
1.1 Yes, it seems to be a small issue with the theme. We will fix this in the next update (probably in 8-10 days).
1.2 Yes, woocommerce pricing filter doesn’t work after AJAX page reloading. For this purpose we created our own price filter widget. You need to use our own widget if you going to keep ajax reloading.
1.3 Also replace woocommerce layered navigation filters with ours.
2. Unfortunately, there is no such option in WooCommerce.
Regards