If a file in SharePoint library has been downloaded 5 times, then I need get that download count of the file.
Additionally I need to get the same for counts of editing done for the file.
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Use versioning, and show the version number. When using only Major versions, the version number will incrementally increase +1 each time the document is revised.
Note: this isn't available for O365/SharePoint Online!
In your Site Collection's root's site settings, navigate to Site Collection Audit Settings. Enable the auditing for at least "Opening or downloading documents, viewing items in lists, or viewing item properties" of "Document and Items"-section. The actual Audit Logs can be accesses also at Site Collection's root's site settings by navigating to Audit Log reports.
There isn't a trivial way to show this number directly in your SharePoint library by the documents. Through manipulating the Audit Logs and mirroring them to SharePoint, the properties (title, download count) maybe could be associated with your document library's documents using Lookup Columns. However, I'm not aware of a documentation doing this, nor have I done it myself.