İf u say verb+'ka' mostly u suppose that the action can be done easily, without much effort. f.e. А сходи-ка в магазин. implies - the store is not far, it won't take you much time to do that. There's no matching word in English, probably in Arabic neither /ba2a has another meaning/. In Turkish it's close to verb+'iver'

يا سﻻم، بص ماما ( امك ) جات بقى ما تفتح فمك انت بقى المشكلة و ما فيها الجمل مليهاش ترجمة مباشرة فاهمانى؟

-ка выражает смягчение или неформальность просьбы, приказа либо требование ускоренного выполнения ◆ Поезжай-ка ты в деревню!

It's commonly used when talking to babies, and forms a specific tender or caressing "babyish" style, I don't know how to name properly such style. "Давай-ка кашку покушаем, давай-ка пописаем." Usually is said with a specific sweet vioce. It's obviously so in your case.

it expresses stimulation