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.
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.
Nilikula halafu niKAkula would be correct. The 'ka' shows the sequence from cooking to eating
Nilipika (halafu) na
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.