Can I export all files/folders and account details/settings from my Dropbox account?

While syncing the files is the best and easiest option, if you're comfortable with command line or terminal commands you can also use dbxcli to download files directly from Dropbox.

Thanks for posting here, myfirstbox! 

At the moment, you can’t export all of your Dropbox account details, except for the invoices/receipts for your Dropbox payments.

When it comes to your files/folders though, you can download all of them from Dropbox this way (after downloading your files, you should still be able to see their original modification dates, file type and size). 

Let me know, if you need something else.