Computation Tree Logic and its Temporal Opeators
First, a small comment - the $F$ operator comes from the word "future", rather than "finally", although it is indeed very tempting to say "finally".


The semantics of $Fq$ with respect to a computation $\pi$ is:
$$\pi\models Fq \iff \exists i\ge 0, \pi^i \models q$$
Thus, the 0th suffix is also considered, so if $q$ hold immediately, the formula is still satisfied.
Observe that you can capture the notion of "strict future" with the formula $XFq$.
The formula states that along every path ($A$), every state $s$ satisfies ($G$) the following: if $q$ and $r$ are true in $s$, then in every path starting from $s$, $q$ eventually appears.


I think this is what you meant in your second option.