Sijambo is not really a verb. It is the noun 'jambo' which means problems / incidents and the first person sg negative prefix 'si' - I don't have
In other words 'sijambo' means 'I have no problems' meaning 'I am fine'.
That explains also the the question:
Hujambo ?-You (sg) don't have problems? - Are you alright?
Hamjambo? - You (pl) don't have problems ? - Are you (pl) alright?
and the answer to the last one:
- Hatujambo. We don't have problems - We are fine
That's a good question!
It's not true with "have". The na is basically just "with". The infinitive is kuwa na, literally "to be with" (not kuna). You'll also notice that it doesn't have the tense prefix either. Essentially, it's not a verb, it's a preposition that takes verbal prefixes for the present tense.