Translation:I went to the farm then I harvested tomatoes.
'Shamba' = farm or garden, 'Shambani' = at the farm, or (at the garden). What you have written "Nilienda shamba halafu nilivuna nyanya", literal translation is 'I went farm then harvested tomatoes'. -ka is like a transition of doing word. If you wrote 'Nilienda shambani halafu nilivuna nyanya' is okay but native speakers will notice you're not speaking like a native.
Indeed 'pick' rather than 'harvest'
since 'halafu' connotes subsequence - like: now that I was at the farm, I gathered SOME tomatoes.
implies an undertaking to reap ALL the fruit - if it were, say:
"Nilienda shambani kukavuna nyanya,"
but that's not what it says here.