your first step, adjusting permissions, should fix the "access denied" problems once you get that correct.
The second issue, that files are deleted immediately, sometimes occurs when File Sharing is enabled. File Sharing creates a classical "multiple Readers and Writers" issue.
Maintaining File status for multiple Readers and Writers is very complex. The way MacOS deals with that is to immediately delete the file.
This is because Trash-ing a file normally only sets the 'In-the-Trash' bit, and adds the file to a list of Items 'In-the-Trash', which is generally local to the Drive where the file resides. The file is not moved or changed otherwise. Making certain every remote reader knows the 'In-the-Trash': status of every file being shared proved overly complex, and the solution is simply to delete the file immediately. In that way, the file status is never in doubt for any Reader or Writer, local or remote.