(b) That's right. A partnership is not considered to be a legal entity that is separate from its members, and the firm does not pay tax on its income. However, a partnership must have its own Tax File Number and the firm must lodge an annual income tax return, showing its annual income and how that income is to be shared by the partners.
The tax on that income is then paid by each of the individual partners, according to their share of the income, and at their individual marginal tax rates.