Does "Γιατί αυτός φοβάται" mean the same thing?
Yes, they do.
Φοβισμένος = afraid.
χαρούμενος = happy.
Does Μένος indicate mood (a mental or emotional state)?
Just a state. The "-μένος" ending denotes the past participle of a verb. (Φοβάμαι, Χαίρομαι, as per the examples you have provided).
Why is he fearful. Acceptable?
Yes, thank you. I've added it.