Problem:
login account, the registration form is not displaying on a page/post

Solution:
Can you please go to:
=> Toolset => Access Control => Toolset Forms tab

And then make sure that you grant the permission to your desired form to be accessed with guest user.

Relevant Documentation:
=> https://toolset.com/course-lesson/controlling-access-to-front-end-forms/

Problem:
Using a form or a content template in a widget

Solution:
The thing is that Toolset do not control the header, footer or sidebars. You can control few theme options of header, footer or sidebar if you are using integrated theme then you will see few theme options.

So, there are two ways, either you should create a content template where you should add a two column grid and add the from on one column and your desired content on another column.

You can find the proposed solution in this case with the following reply:
https://toolset.com/forums/topic/using-a-form-or-a-content-template-in-a-widget/#post-2034995

Relevant Documentation: