Breakdown of Он очень скромный человек.
он
he / it (for a masculine noun) / it (for a neuter noun)
человек
person
очень
very
скромный
modest
Questions & Answers about Он очень скромный человек.
Since the sentence starts with Он (He), could I use мужчина instead of человек here?
You could say Он очень скромный мужчина, but it focuses too much on his gender, sounding a bit like 'He is a very modest adult male.' Человек (person) is the standard and most natural way to describe someone's general character traits in Russian.
If I wanted to say 'She is a very modest person', would I change the adjective to feminine?
No, because the adjective must agree with the noun right next to it. Since человек is a masculine noun, it stays Она очень скромный человек. However, if you drop the word 'person' entirely, the adjective then agrees with 'she' and becomes feminine: Она очень скромная.
Does скромный only mean 'modest' in the sense of not bragging?
It definitely means 'modest' or 'humble' in terms of personality, but it is also widely used to mean 'unpretentious', 'simple', or even 'shy'. For example, if someone invites you to a скромный ужин, they are offering you a simple, modest dinner without anything overly fancy.