Hello,
01. Yes — you can add an “In stock” filter and additional filters to the shop sidebar.
Navigate to Appearance > Widgets > Shop page widget area and add the WoodMart Stock status widget.
See the screenshot for better understanding: https://postimg.cc/jwLYb6Vc
If you want to add more filters, In the same Shop Sidebar widget area, add more widgets that you want
Please check this manual: https://xtemos.com/docs-topic/widgets-and-sidebars/
To change product sorting on shop page, Navigate to Appearance > Customize > WooCommerce > Product Catalog > Sorting Options from where you can select the sorting method you prefer: https://ibb.co/CK9TQdd
02. Please go to Theme Settings >> Product Archive >> Page Title >> Disable the Categories in page title option: https://ibb.co/RGJ8qsMc
If you want to change the background color or add a background image, navigate to Theme Settings > Page title > add the background image or color. These settings will be used for all page titles.
Also, if you want to change it only on the shop page, navigate to Pages > edit page > scroll down to Page Settings and check the Page title and add the background. https://xtemos.com/docs-topic/options-for-pages/
Best Regards