You can configure the default popup width and height for each form. It is not possible to save custom settings for each user.
I feel your pain. I also understand your test-user's issues.
No, there is not a way to store 'settings' for a specific user at this time.
The default UI behaviour of Mendix apps is based on the principle of "What do most users expect?". Or, more accurately, "What can most users work with?". The Mendix R&D team has, over the years, received an overwhelming amount of user feedback on UI requirements.
The ability to store the state of grids and pop-ups per user-session comes up regularly as a feature request, but it is never high on the list of must haves. It would only add functionality for a small subset of users, require a large amount of engineering effort and make the app behaviour unpredictable for the majority of end-users - something that would have to be compensated for with even more modeling options.
Sorry I can't give you a solution for your test-user.