Hi Bob-thanks for your questions. Here’s the answers:
1) No, once your application is filed you do not have to remain in country. You may leave and return with the multi-entry visa, and your attorney should keep you advised of the status of your application.
2) Once you have your visa and cedula you may be out of Panama for up to two years without losing your status. So once you have your visa you may leave the country and return before two years have passed with no problems.
Be sure to visit the Insider pages where you’ll find lots more information about residency and visas, here:
https://internationalliving.com/country_clubs/panama/visas-and-residence/
Hope this helps. Chao, Linda