As it's closed, I can't add any comment so I will answer to your questions here:
-Disabling literally all plugins didn't fix the issue. It seems that there is no conflict between my theme/plugins and Toolset.
Please help me find a fix to the problem. I still can't edit custom archives.
2)
The issue seems to be caused by the theme you are using. I see the following JS error on the browser console:
TypeError: class constructors must be invoked with 'new'
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When I disable all the thrid-party plugins and switched to the default theme I can see the archive is working. As you can see with the following screenshot:
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