How do I reorder & better organize folders in folder panel? (Elements 2018 Organizer)

You have chosen to manage your photos from the folder structure.

Yes, Elements can display the folder structure in a similar way as your Explorer or Finder. You can even rename or move subfolders if you want.

But the folders tree in that panel is just like the one in the Explorer: its sort order is based on the alphabetical order as it is indexed in the operating system.

Maybe take the time to consider why most users with drastic organizing requirements don't use primarily a folder structure, they use catalogs managed by a database, like Elements or Lightroom.

Any folder tree structure can easily help if your structure is simple: date or events for instance. Many users like you are happy with a double structure, date plus events. But like you, they can't manage easily more criteria at the same time, date, events, persons, places, authors... If your Picasa offers the ability to move 'folders' as you say, chances are that it does not physically change the sort order when you are viewing it from your Explorer. It keeps your custom sort and tree order in a database like Elements does for albums.

The main advantage of catalogs is that you are not limited in your criteria. You can search from several criteria at the same time.

The second one is speed because of the indexing or your keywords, even with very large libraries (more than 100 000).

The data structure is not based on the physical location on your drive, it is virtual and totally flexible.

Just try with albums and create categories, subcategories and use the option for 'manual' sorting. I imagine that is what you are after.

But once you are satisfied with the way your files tree is displayed, also take the time to test the various search and display tools in Elements. Also test the new enhanced text search you get by clicking the magnifier glass on the top right. Retrieving complex queries in seconds is unbelievable. With my 70 000 items, I can retrieve immediately files from various criteria, including parts of text strings in a caption or a note...