And, is liquid paraffin a "mineral oil" suitable for lubemaking? ... Yes, it's the same for the most part. Just a different layer in the distillation towers.
So far I've done fine with ATF, but would Baby Oil be better? ... No, unless a better smell is justified. However, ATF has some synthetic slickies that you won't get with just plain ol' mineral oil, paraffin, etc. Is it better? Maybe, just depends on application.