'Shared With Me' folders may be shared with a simple right-click, SHARE selection.

From there, you may select ADVANCED settings to discover the Owner of the item.

If you are the owner and you are sharing with others, deleting the file will delete it permanently for everyone.

If you do not own the item, you cannot delete it permanently. Only your copy will be deleted.

For more about Drive documents visit https://support.google.com/drive/answer/2375057?hl=en