At school, we were taught this method of giving a value of voltage to
points in a circuit.
I believe there's a misconception here that may be the root of the remainder of the questions (of which there are too many for one post).
I assume that, by "voltage to points in a circuit", you're referring to the concept of a node voltage but, conceptually, a node voltage is not a 'voltage at a point in a circuit'.
Rather, a node voltage is the potential difference between that node and the 'ground' (reference, datum) node.
The node voltage of the reference node is zero since the potential difference between a node and itself is zero.
For a physical picture, imagine placing the black lead of your voltmeter on the reference node and then placing the red lead there too. Your voltmeter should read zero volts.
Now, place the red lead at a different circuit node. The measured voltage is the node voltage for that node. Again, this is not a voltage at a point in a circuit but the voltage between that node and the reference node.
However, I do not understand how we add up the voltages and I also
don't understand why the voltage between the two batteries is V and
So, for example, if I place the black lead of my voltmeter at the reference node ( marked with $0$ in your diagram), and I place the red lead of my voltmeter at the node between the two cells, I should of course measure the voltage $V$ across the battery. That's why that node has voltage $V$ assigned; it is the voltage between that node and the reference node.
Now, assuming identical cells, the voltage across the left-most cell is $V$ and that means that the $+$ terminal is more positive by $V$ than the $-$ terminal. But we already know the $-$ terminal is connected to the node with node voltage $V$ thus, the node voltage at the $+$ terminal is $V + V = 2\cdot V$.