is there an API for GIT (C++ or other languages)
Git already has two layers: The plumbing (which you may be interested in) on top of which is built the primary porcelain which provides the user interface. If you want to implement something like git-commit but with slightly different semantics all of the underlying programs like git-write-tree and git-rev-parse are there for you to build on.
There's already TortoiseGit, among other "friendly" interfaces. Don't re-invent the wheel, start by researching what's already available.