Quick question: Could the second clause also be written "hatungalikula" to have the same meaning?
Yes, I believe the form with -singali- is considered more standard but the ha_ngali- form also exists (the same goes with -nge-).
Why is it kisingalipikwa and not kisingalipika? Because the verb is kupika so I am wondering where the extra letter is coming from.
-wa is the passive suffix (pika = "to cook", pikwa = "to get cooked").