Is there something for a local repository to:
1) show how frequently all the files and directories of repository are changed;
2) for a certain file: show how frequently the lines and paragraphs are changed?
Optionally with a timelapse.
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For option 1 (show frequency of file/directory changes), Gource is an open-source tool that creates visually interesting displays of git project histories, though it's geared more towards looking cool than doing analysis of the changes. You supply it a project and it will generate an animation of the file tree, showing how often files are touched by commits.
I don't have a good suggestion for request 2 (line by line historical information), though if you're up for a coding challenge you might be able to adapt the gource source code to your needs.