Headcanons!
Loz's mental state (headcanon edition)
Loz is often described as "missing something upstairs" and let's face it, throughout the entirety of AC, Loz acts like an adult-sized kid. He cries, he seems to think fighting is playing, and he pines for Mother.
The way I see it, Loz is just a really big kid. He sees the world as his playground and the opposition his toys. He doesn't seem to have a sense that fighting actually isn't playing and is actually pretty destructive. However, while he may mercilessly beat his opposition and even torture them (sorry Elena), he doesn't want to kill them because then they can't play again. Breaking his toys just isn't fun in the end, and while it might seem like a good idea, he probably realizes it won't be fun down the road. I don't particularly see him as the murderous type. He just doesn't have that sort of mental capacity.
For him, family is always first, especially Mother. I don't think he really understands what mother is or how to find mother, but that he has to find her. I don't think he fully understands why either, other than a child wanting Mommy. He knows it's important, particularly to his brothers, and wants to reunite with everyone. Big happy family and all. He really doesn't show any understanding of the magnitude of what he's doing and how it'll affect the world around him. Much of what he does is really to fulfill Kadaj's plan for the Reunion.
Age-wise, I see Loz being about 2-5 mentally. He is perfectly capable of forming sentences though when he speaks (at least in the Japanese version), his sentences are informal and sometimes a bit rough. Being that age-ish, he doesn't really have much of a comprehension of the world around him, save particular things he should know, like materia, Geostigma, and the Reunion (somewhat). (For reference, his and Yuffie's conversation about the uterus and what it is (no, it's not armor).)
Also being that age, Loz seems prone to anger, not quite rage but more along the lines of a minor temper tantrum. He gets frustrated when Yazoo mocks him for crying, and even is sharp and quick to say he isn't crying. And with the strength he has (thanks to being that aspect), this could be a dangerous thing. I imagine he's punched through enough doors in frustration and anger, maybe flipped a few tables or kicked over trees.
Not necessarily an age thing, but Loz seems to show no fear. I don't really see him as being afraid of everything and probably thinking he's invincible (much like kids do). With the way he survives things (like getting bombed on the highway and thrown around in his fight with Tifa) it's no wonder he thinks this way. In regards to being fearless, think of how he motorcycles off a cliff to chase after Cloud. Who in their right mind would do that?
TL:DR: Loz is 2.