Problem:

The issue here is that the custom fields for Types aren't showing up in the Elementor Dynamic content settings.

Solution:
This is a known issue and have setup and errata page for this to provide you with more information.
https://toolset.com/errata/elementor-dynamic-sources-not-working-when-selecting-toolset-fields-as-source/

Unfortunately there is nothing that we can do on our side for this one.

Problem:

Style container block with custom CSS class names.

Solution:

You can edit the page/post, find and select the "Container block", in the sidebar, section "ID & Classes", setup your custom CSS class names, see my screenshot:

https://toolset.com/wp-content/uploads/2021/04/2014395-container_block_css.jpg

Then use those custom CSS class names to setup your custom CSS codes.

Relevant Documentation: