All correct, apart from the exams example.
'I'm happy about your exams.' is ok. As Joseph said, you probably mean 'exam results', but in the context, it's clear what you mean.
You wouldn't say 'I'm happy for your exams'. As in your first example, you can use 'happy for' followed by a person, but not usually by an event, situation or object. In this context, 'happy about' is the correct form - 'I'm happy about your new job'. for example