"Shut your mouth, tits."
Yes on older- Demihumans and monsters grow up physically with time, but also with levels. Thats explained canon in the Light Novels and I believe in the manga too. Humans dont appear to have that effect in general, but (to the point I've got to in light novels) it isnt (quite) definitive yet that the Shield Hero's human slaves dont either. Its unclear if levelling affects the mental maturity of demihumans and monsters at all; At least a small amount of advancement seems indicated, but certainly not full maturity.
As to the things people didnt want spoilers for, I shall not spoil them, but the manga and LNs are available online for those who wish to read ahead.
Manga-
The Rising of the Shield Hero
Light Novels-
Sword and Game: The Rising of the Shield Hero ToC (Note- a few of the links that take you to the next chapter when you finish reading the current one dont work, so you'll have to use the main index to get to the next chapter when you find a broken link. 2 such broken links so far for me, up to chapter 146)
The LN and the manga diverge massively in the not that distant future. The anime seems likely to follow the manga, but again its too early to say for sure.