Although I might be wrong, I'm pretty sure you dont need a conjunction as long as you don't use a comma between the two subjects and actions.
Would 'kisha' instead of 'halafu' mean the same thing here?
Nilikula halafu niKAkula would be correct. The 'ka' shows the sequence from cooking to eating
Nilipika (halafu) nakala.
The "ka" tense doesn't trigger the "ku" to appear. Also, the -ka- makes the word halafu unnecessary, although you can still use it if you want to emphasise it a bit.
That's right! My mistake. I grew up in Nairobi and the casual speech isn't as gramatically correct as it should be!
I cooked and then I ate = conjunction required for two actions
No. "Then" on its own is able to fulfil this role. It may not be present in your dialect of English - you may need the "and", and it should be accepted, but just "then" is perfectly fine.