Short answer
Family members on a Student visa may have work limits. Adult family members are generally limited to no more than three months of study or training in Australia.
Family members generally cannot work in Australia until the main student has started their course.
Some family members may also have a 48-hour-per-fortnight work limit. Volunteer work may be treated differently in some situations. Family members should check the exact rules listed on their own visa.
For study, adult family members usually cannot study or train for more than three months while in Australia. If they want to study longer than that, they should consider applying for their own Student visa.