Yes, you must go through this process because your visa will be checked in paperback form on different platforms and by different officers.
No, people with a green card can travel to Belize without a visa for up to one month.
You can get a Belizean visa by going through your country's embassy or consulate
The processing time for Belize visa applications for short stays may take up to a month. However, to obtain a long-stay visa for Belize, you must allocate at least four weeks of your time.
It is possible to stay on the island of Belize for up to ninety days every three months and one week. You will be allowed permission to remain in the nation for the time indicated in your Belize visa after successfully applying for and being granted a Belize visa. It is conceivable that you will be given ninety days, but this is not guaranteed.