Files not sharing and not deleting, showing different content on sender and receiver

Were you the owner of the shared folder? You should be able to at least remove it from your account to free up quota, even if you can delete it.

I was and still am the owner of the folders that gurgled up from the past when I went into that link. These are old folders from in some cases years ago that I should never need again, and it's telling me I don't have "permission" to get rid of folders which nobody has any use for including me. I don't get why it won't let me delete.

I am not the owner of the account that could not see files I uploaded (the recent issue). That folder was made for my use by the other party. But that also has files Dropbox won't let me delete. In both cases I'm referring to 'permanently delete' which I never had any issue doing before on either account.

Regarding the desktop, they're most likely referring to the Dropbox desktop application, which would allow the folders to sync to your machine. 

I'm afraid I don't begin to understand what "sync to your machine" means. Basically per my understanding what I do is I generate files, I lay them on a "table" (a Dropbox folder) and alert the appropriate party that it's there for them, they come to the "table" and pick it up, and that's it. When I know they have picked it up I take it off the table (delete). There's no "sync" of anything involved. That's maybe why I don't get the distinction between "using the website" and "using the app". Maybe, I don't know. And I'm not keen to go into that without knowing the consequences.

I'm really wondering if something has become corrupt and if I should actually delete my entire account and start over. If I do that can I re-establish a new account and re-establish access to the shared folder the other party made for me? Would I need a different email to do that? Or is it possible to simply wipe the account clear of everything? All the files I have in there now are ones I can reload, so there's no issue of losing anything. I just want to know I won't lock myself out of the car so to speak...