However, is it good for those arguments to be the names of the various tables and columns of the database? Or should that information be hidden/encapsulated by the API ?

One way or the other, there is going to be a large API. The requirements of the program dictate that. I mean, there are a large number of logical operations to do on the data. Whether there is a different function for each, or fewer functions with different arguments, it's still a large API. The syntactical appearance is different, but the the logical API is still there.

I think I'm leaning toward different function names, as explained elsewhere. Maybe this would be a good subject for another SoPW post.