As the title above, why do japanese locals remove theいfrom the いadjective when speaking. For example, I have heard words like 早、やば、高 being used when speaking. Is this only used amongst friends (very casual), or can it also be used in formal situations?
I know that removing the い from the adjective and appending a さ turns the adjective into a noun. But if さ is not appended, will it stay as a verb, rather then bring turned into a noun?
It's uttered as a colloquial, casual and exclamatory phrase. It's typically used in response to a situation/stimulation that strikes you suddenly. っ is often added after the stem.
- 高っ! (Wow,) it's expensive!
- やば(っ)! (Wow,) this is bad!
- 痛っ! Ouch!
- きもちわる(っ)! Gross!
In formal settings, you should generally avoid this, but no one would blame you for saying 痛っ or 熱っ if you are really suffering.
Related: In real life, do Japanese speakers exclaim things like 熱っ！ or 痛たた… or 寒！?
Not all i-adjectives work like this. We rarely say 悲しっ or 寂しっ, presumably because these are not "sudden" stimulation. Most adjectives used like this are negative ones, but there are exceptions (うまっ, 安っ, ...).
