I worked for a database company for three years and I most frequently heard the word used as a noun, something like this:
- "The database will confirm a commit by doing X"
- "When talking about how the database does commits"
In this case, "a commit" is understood to be a piece of data that has been written to memory/disk or similar. Hence I would say that your second option would become
- How the target DB engine handles a data commit (singular)
- how the target DB engine handles data commits (plural)
The verb form which you have listed in 1 and 3 was not something I heard as often, but when I did hear it used, it was usually in the third form you listed above, that is: "committing". I don't think I have ever heard anyone use the first version you listed (commitment) in conversation.
Personally, I think that the reason it sounds odd to me is simply because commitment is a term more frequently used to describe the human capability to commit to a task, person, job rather than a technical term. However, in the right context I would have no problem understanding the terms as it pertains to databases.
With that anecdotal, personal evidence out of the way, I will note that searching for "data committing" and "data commitment" in a database context in Google returns plenty of relevant results. In fact data commitment returns twice the number of results. Hence both terms are clearly used as verbs and are acceptable as such.