I was previously confused, and, now I'm increasingly confused :/
Are such powers solely listed in the constitution? Or are they powers the Commonwealth possess and can in a way influence (e.g. s.109 override)? Or both?
Ok the Commonwealth can only fully exercise these specific powers if they can pass a High Court ruling. So although s51 might grant the Commonwealth some rights, if the High Court interprets the wording/nuances of that wording differently than what is literally written in the Constitution, the Commonwealth cannot exercise those rights.
So to answer the first part of your question, no, the Constitution is not the sole source of the Cwlth Parliament's specific powers. Common law (ie. precedents) also determine how the Commonwealth can exercise those specific powers (to answer the first part of that question).
Your second part of the question is quite confusing; but think of it this way: any right (eg. public transport or IVF) that is NOT listed in the Commonwealth Constitution CANNOT be exercised by the Commonwealth Parliament. This is known as a residual power (given to the States) and the Commonwealth cannot exercise these rights, so yes you can say that the Cwlth Consitution lists all the powers that the Commonwealth possesses. The Commonwealth parliament can only make laws that are listed in the Commonwealth Constitution, or other rights given to it by the High Court through case interpretation.
The last part of your question is about s109. As Chasej and I have stated, there are two types of Commonwealth (specific) power. They can either be exclusive (only Cwlth can exercise) or concurrent (shared between state and Commonwealth). Since there are *some* rights that both Commonwealth and State can occur, what happens in a concurrent power when the State disagrees with the Commonwealth? We can't have two different laws that say different things, right? How would we know which one to follow? This is where s109 comes in. There are two "tests":
1. A High Court/Federal Court case is initiated, by a party affected by this inconsistency
2. The High Court/Federal Court agrees/interprets that the inconsistency exists.
In *any* case, the Commonwealth law will prevail over the State law, in areas of concurrency, to the extent of the inconsistency. So, basically s109 is essentially just a "troubleshooter" or resolver of conflict in the rare occassion where in concurrent powers, state and Cwlth law clash.
Remember, s109 only applies in areas of concurrent powers. It's not an overriding provision where the Commonwealth can make some random law (eg. terrorism laws) and override the States in any instances. Why? Because terrorism laws is not a specific power - it's a residual power - only exercisable by the states.
Glad to help with any further question/ if anyone wants to correct me if I have said anything incorrect.