I am able to create Experience Fragment using Experience fragment template(OOTB) in Classic UI. But, I am not able to see Experience Fragment template when I try to create Experience Fragment in touch UI.
Also, I am able to create Experience fragments inside Experience fragments in ClassicUI but in touchUI I am able to create only variations inside Experience fragments.
In CRXDE, go to /content/experience-fragments and check the "cq:allowedTemplates" property
Also to add an experience fragment inside an experience fragment, edit the template and add the "Experience fragments" in the Layout container policy. This is similar to adding the allowed components in the container policy.
Also, it is recommended to try all these in touch UI as they are the latest functionalities by adobe.