Hello Gregor,
1. You can modify the search form template file and reorder the fields as you wish. In the template file you will find different functions that populate the different form fields.
The search form template files can be found in geo-my-wp/plugins/posts/search-forms/
2.
any option to preserve search selection on form for users?
Not at the moment unfortunately. Hopefully I can add this feature to a future release as it has been requested before.
Let me know if you have an other questions.
Regards,
Eyal