Hi,
We checked your links and the design you have used.
Functionality wise there is nothing new only the design is different.
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For this you'll have to create a child theme and then change all the designs.
For menus there is nothing new, you can use the category mega menu and posts mega menu, here are the tutorials:
Sub Category style:
https://vibethemes.com/documentation/wplms/knowledge-base/mega-menu-sub-category-style/
Category post style:
https://vibethemes.com/documentation/wplms/knowledge-base/mega-menu-category-posts-style/
For teachers menu and the other menu, you can create a simply mega menu, refer:
https://vibethemes.com/documentation/wplms/knowledge-base/setting-up-mega-menu-in-wplms/
But in this you'll have to create all the custom links for all the teachers.
For featured block you'll have to create a new custom featured block, refer:
https://vibethemes.com/documentation/wplms/knowledge-base/creating-custom-featured-block-style/
For all courses page the filters are already there you'll have to change the style for showing it, and you can change the course directory template using the child theme to show it according to your requirements.
Similarly the single teacher's page can also be overridden using the child theme.