Given this transition system, for which states are these (very basic) LTL formulas fulfilled?
Note that questions of the form "am I correct" are generally not acceptable on this site. Still, your question shows an effort, so here are some answers:

As for your classification to LTL/CTL - you are correct.

Let's look at (b) - it interprets to "always b", which means that in every path starting from the state, b must always hold. This is not the case for any state in the system (since every path eventually reaches s2, in which b does not hold).

As for (e) - it means that in every path, in every suffix, $bUa$ hold, so in every suffix it is true that b holds until a holds. In this system, you are correct that all states satisfy this.

(c) is perhaps easier than the other two - it reads as "next next a", and a state satisfies it if in every path from it, in two steps you will reach "a". In this system, every path gets within two steps to s2, s3, or s4, all of which have "a", so the formula holds.