Readdle cross-app integration: Documents and PDF Expert
The Documents app works very well together with the iPhone and iPad versions of PDF Expert (by the same company). You do need to go through the share dialog and you could use another tool such as PDF Pen Pro if you prefer or wanted a universal app for editing PDF that you locate and move using Documents app.

Since iOS abstracts away the filesystem, unless you are careful to push changes back to a cloud storage location, you can get files duplicated, wrong versions and revisions. I don't think there is a silver bullet solution at this point for iOS file management other than using a single app that syncs directly to a shared folder.

Luckily, PDF Expert does just that and works with a plethora of server backed storage options - Dropbox, WebDAV, Google Drive, FTP / SFTP, Office 365 / SkyDrive, Box, Oxygen and Huddle currently:



Even better, you can set up sync to minimize the chance that you will forget to upload or download a changed document.