Learn Farsi: او مجبور نیست.

This sentence just states a general condition: 'He is not obliged.' You only need to add ke (that) and a subjunctive verb when you want to specify what action someone is obliged to do. For example: او مجبور نیست که برود (u majbur nist ke beravad), meaning 'He is not obliged to go'.

How is majbur nist different from using nabayad (must not)?

They mean very different things. nabayad shows a strict rule or prohibition ('He must not'), while majbur nist shows a lack of obligation ('He does not have to', meaning he still can if he wants to). This is a common mix-up for English speakers.

The lesson mentions majbur shodan (to become obliged). Could we use that here instead of the 'to be' verb?

Yes, but the meaning shifts. majbur nist uses the negative 'to be' verb to describe a current, static state ('He is not obliged'). If you used the present negative of 'to become' (majbur nemishavad), it would mean 'He does not get forced' or 'He won't be obliged,' focusing on an event or change rather than a state.

The translation says 'He is not obliged.' Can او (u) also mean 'She is not obliged'?

Yes. The Farsi third-person singular pronoun او is entirely gender-neutral. It translates to 'he' or 'she' depending entirely on the context of your conversation.