Hi Robert
I'm not aware of any issues with either the themes or the plugin, and the only way to answer the question about whether Toolset works with them is to try and see.
Start with the question of theme compatibility. Toolset is compatible with most themes out of the box, with a couple of provisos.
Layouts effectively has "Full" and "Lite" modes. For the full mode, themes need to be integrated to work with Layouts, which involves making relatively modest edits to the theme PHP templates described here: https://toolset.com/documentation/user-guides/layouts-theme-integration/. We provide integration plugins to do that for you for the most popular themes.
With integrated themes you have full control over the design of the entire page, including the header, footer, and sidebars, in addition to the main content area where your posts are displayed.
In the lite mode (when not explicitly integrated) Layouts behaves like most page builders and can only be used to edit the content area of the page: the header, footer etc. are rendered by your theme.
That's also how Views works (and you can use Views without using Layouts), it renders only the content part of the page.
Specifically it takes over the rendering of the part of the page generated by the_content() function. That is the standard way most themes render the post content.
Non-standard themes that use a custom function to render the post output need special handling to work with Views (or Layouts in lite mode), as described here: https://toolset.com/documentation/user-guides/editing-view-templates/theme-support-for-content-templates/
Not having a copy of your theme I can't say whether it is a standard theme or not, but very few themes cannot be made to work with Views as described above.
Regarding the plugin, again, I'm not familiar with it, other page builders work okay with Toolset although do sometimes need special handling. If there is something specific that you are trying to use the plugin for which isn't working and I can investigate further (you'll need to provide me with a copy). As Layouts is a page builder, adding another page builder into the mix may create issues, and it depends on exactly what you are trying to do and what your preferences are: if you like that page builder it may make sense to not use Layouts and use Views in conjunction with your preferred page builder, or you may find you can do what you want with Layouts and Views and don't need the additional plugin.
So, having said all that, can you describe what exactly you want to do and I'll make sure you are doing it right, and if it doesn't work I can investigate why.
(I didn't understand "It seems to build ok but does not display within my them properly".)
- You have a custom post type called Case Studies
- You are using Layouts to create a template for single Case Study posts, which, because your theme is not integrated, will only take control of the content area of those posts, and the theme will render the header and footer.
What is the problem you are experiencing?