This thread is resolved. Here is a description of the problem and solution.
Problem:
If you export a Toolset Form from one site and import it to another any custom markup etc. is lost, the form reverts to the default state as if it had just been newly created.
Solution:
This is a confirmed bug that is fixed in Forms 2.3.4
This support ticket is created 5 years, 8 months ago. There's a good chance that you are reading advice that it now obsolete.
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Issue One
If I create a new User Form, custom user fields are shown in the drag & drop window but are not available in Expert Mode until the form is saved.
Issue Two
If I import User Forms from a zip file created using Toolset's Export/Import tool (not Module Manager), all customised content in the Form Editor is lost.
I have yet to test if the same issues apply to Post Forms but will raise a separate ticket if I find they do.
For some reason your debug info doesn't include the Toolset plugins so I can't see what versions you are using, but with the current versions I couldn't reproduce issue #1.
See the three screenshots.
I made a new form, which opens in the drag and drop mode and includes my "Favourite team" custom field.
I switch to expert mode. The markup for this field is already included. And if I use the Add Fields button, it is there, available for me to insert.
I went back and re-created a new user form which worked this time so not sure what happened there. I was about to re-check the import bit but you beat me to it!