Is the truth value of $(F \iff T) \iff (T \iff F)$ True? I think $(F \iff T) \iff (T \iff F)$ is true, but would like some confirmation.

Yes, it is indeed true. Remember that "$A\iff B$" is true if and only if $A$ and $B$ have the same truth value - both true, or both false. So both $F\iff T$ and $T\iff F$ are false, and so in turn "$(F\iff T)\iff (T\iff F)$" is true.
Here's a fun fact (you can check it for a few small cases, and then prove it by induction on the complexity of the formula): suppose I have a formula built out of $\iff$s (like yours). Then it's true if and only if an even number of the components are "false" (note that zero is even); so e.g. $$(T\iff F)\iff ((F\iff T)\iff (T\iff F))$$ is false ($3$ Fs), but $$((T\iff F)\iff (F\iff F))\iff ((F\iff T)\iff (T\iff T))$$ is true ($4$ Fs).
