There is a fine Wikipedia page for this IC. You can answer all the question from it.
Also is this the correct diagram for the IC?
It is functional equal.
If you compare it with the diagram of the Wikipedia page or, for example, with the TI data sheet, you will find that the flip-flop is commonly drawn with swapped set (S) and reset (R), and with an inverted output. The latter compensates the swap.
The meaning of correctness depends on the usage. It is fine to understand its function. But to map actual chips, it can be incorrect.
- Q′ = 0 → Final output high, capacitor charges
- Q′ = 1 → Final output low, capacitor discharges
As you don't define the circuit around the 555, we cannot check your conclusion about the capacitor. You can use the 555 for more then astable or monostable oscillators.
Assumed that you mean the common astable configuration, the relation between output and charge/discharge is correct. However, as your diagram shows a direct and non-inverted connection between Q' and output, your assignments are swapped.
- Q = 1 → transistor on → capacitor discharges → output low
- Q = 0 → transistor off → capacitor charges → output high
This is correct.
Compare it to your statements about Q': you cannot have the same result for Q = 1 and Q' = 1.