"How are you students?"
I heard that a lot of Swahili words are made up of other parts, maybe I missed it, but how would you break up "Hamjambo"?
If I understand it correctly, ham- is the negative prefix for the 2nd person plural. (Or it's an abbreviation of hamna 'you do not have'.) When you add that to -jambo 'thing, matter, affair' what you're asking is something like "Is nothing wrong?" https://forum.duolingo.com/comment/21139696
Yes, it is an abbreviation of hamna. On a verb, ham- is the second person plural prefix, but jambo is a noun.
If you translated that it'd mean "news is you (singular)", which doesn't actually make sense. Habari is for asking about things as a greeting, but it's not a way to ask an individual person or a group of people how they're feeling.
this english statement isnt grammatically correct and therefore is a bit confusing.
I think there's just a comma missing after "you". Makes a lot more sense that way.
No, that is not something you would say in Swahili. Habari ya/za (leo/mchana/etc) is a way to say hello, not an actual question of how someone is.