As James has explained, in theory "Chinese" can be used as both an adjective and as a noun. Nowadays, however, it is always used as an adjective and its use as a singular noun sounds strange. The same applies to most adjectives of nationality except those ending in -an (and those with endings distinct to that of the noun form). Additional note: "Chinese" can refer to nationality and / or ethnicity, while "American" is just a nationality (or perhaps a reference to location).

I think when you say I’m an american, it gives the impression that you’re saying”I’m an american citizen “ as in “I am part of the american community “ However, saying I’m american is a direct reference to your nationality. So when you say I’m a chinese , you’re essentially saying I’m one of the chinese population I’m chinese means nationality. Hope it made sense!

I have tried to find an answer for you because I didn't know the answer to this either! So, you can say 'I'm American' (adjective) or 'I'm an American (noun - American person). You can also say 'I'm Chinese' (adjective) or 'I'm a Chinese', both are correct, however 'I'm a Chinese' sounds strange. It is better to say 'I'm Chinese'. In the past many people would use the word 'Chinaman' however over time this became seen as an offensive word. You can google this term to find reasons for this. For different reasons 'Frenchman' and 'Irishman' for example are not used so frequently, though this is more because the word 'man' is gendered, so it is better to say 'French person'. Perhaps people struggled to adapt to saying 'I'm a Chinese' instead. Also in the UK the words 'a Chinese' is often used as a quick way of saying 'a Chinese meal' so perhaps this is part of the reason. I hope this helps?!

I am an American is just the long way to write it, it's ok, but also I'm American is also ok.

‘I’m an American.’ and ‘I’m American’ have a slightly different nuance. The adjective is descriptive and more neutral. Using the noun is more emphatic - it states that being American is part of your identity. Conversely this noun form could be used negatively by someone from another country - suggesting that the person has the stereotypes associated with being American. You can use the following neutral noun forms for any country: He’s a Chinese citizen. He’s a Chinese national.