what is the difference between "moeten", and "hoeven"? I notice they are not interchangeable, so when do i use which?
The way I see it, iets niet hoeven means it is not necessary to do something, whereas iets niet moeten means it is absolutely required that that something doesn't happen.
Why does moeten force the second verb to be an infinitive?
Because moeten is a modal verb (it indicates whether the action indicated in the second verb is compulsory, voluntary, permitted, etc.)
Why can I not just say "heeft jij werk vandaag?"
That would be heb jij. Also there's a difference between Do you have work? and Do you have to work?. To have vs to have to.
-Moet je werken vandaag?- sounds more natural to me as a native speaker