This is just one of the many examples where I noticed this, but with these words, does that mean I can say something like: 我找到我心里的安宁 or something along those lines and treat it as if it were a noun, but at the same time can say something such as : 他很安宁 and treat it as an adjective? Or should I just use a different word altogether? Thanks for the help
Many words are used as different word type for convenience
For example, when the noun 鑽 (drill) was coined, it was convenient to use it as a verb for 'to drill' as well; when we have the existing adjective 哀傷 as in 哀傷往事(sad past), it is convenient to use it as a noun as in 這份哀傷 (this sadness)
The adjectival marker 的 can turn a noun or a whole phrase into an adjective. Also, many nouns can be turned into adjectives by adding other particles. For example 攻擊(n): attack --> 攻擊性 (offensive) | 戲劇 (n): drama --> 戲劇性 (dramatic). And standard nouns can be used as adjectival nouns as long as it makes sense (it is still a noun, but functions as an adjective for another noun). See How to use nouns as adjectives?
The phenomenon can be found in other languages. Not sure why it surprises you.
Anyways, I just want to comment on your two examples.
我找到我心里的安宁 // a very good sentence. (sounds a bit literary), but you might put it in a proper context or it sounds incomplete. For completion, you might want to insert a 了: 我找到了我心里的安宁.
他很安宁 // 安宁 is usually not used for a person directly，but it doesn't sound wrong and probably your creative writing(?). You can also say 他的心很安宁。今天的夜晚很安宁。or 两国边境很安宁。