Technically, LTL and CTL are incomparable in their differentiating power over Kripke structures. So intuitively, it shouldn't be easier to design one or the other.
However, most people tend to find it easier to think in linear time. Making sure a certain property holds for all paths is easier than studying a branching-time property. In particular, this is because a counter-example for the satisfaction of an LTL formula is a path, whereas a counterexample for a CTL formula may be a tree.
To demonstrate how to approach the questions at hand, let's consider the first one. First, consider what the formulas mean:
$FGp$ means "in every path, after a finite prefix, $p$ always holds".
$AFEGp$ means "in every path, after a finite prefix, a state is reached from which there exists a path in which $p$ is always true."
Now, if $FGp$ holds, then $AFEGp$ must also hold, because in every path, eventually a state is reached from which $Gp$ holds. Thus, our search should restrict to finding a system which satisfies $AFEGp$, but not $FGp$.
To achieve this, we need to at least have a state that satisfies $Gp$, so let's start with that. Take the state $A$ to have the transition $A\to A$, and $A$ is labeled with $p$. Let's also have $A$ as the initial state (this is arbitrary). So far, this system also satisfies $FGp$, so now we fix that by adding a "bad path": we add a state $B$, labeled by $\neg p$ with the transitions $A\to B$ and $B\to A$.
The path $A,B,A,B,...$ does not satisfy $FGp$, so this is good. However, every path eventually reaches $A$, in which $EGp$ is true, so $AFEGp$ holds, and we are done.
