It seem my answers is quite confusing since it wasn’t structured as one cohesive post.
Let start with the short ones.
Also why shouldn't the native people get good treatment in their own country? If I went to China I'd understand I was a guest.
Considering the native people of their own country, who are typically the majority ethnic group, In most cases, the majority ethnic group in a nation tends to hold power and influence over how minorities ethnic are treated as they see fit. You already answer this yourself

, below.
I mean, if you truly dominate another then you can basically do what you want including taking things from them.
Surely we're all typically dominant on our own land, like your own nation or even to some degree your own house.
it depends upon a privileged ethnic group taking cultural elements from an oppressed group in a way that belittles the latter and is often done to enrich themselves and profit off of it. Ignoring this dynamic overlooks critical issues of race and nation
In this context I’m talking how cultural appropriation becomes commodified under capitalism, whether it should get good or bad treatment its depend upon the majority (sound democratic

). Let me give you an example: the so called "Chinese silk dress" (Qipao) are not Han Chinese but Manchu who are an ethnic minority of northern China that came to rule the empire throughout its last 200 years until its fall in the Xinhai Revolution of 1911, after the establishment of the Republic of China, cultural "items" like the Qipao became associated with the broader Chinese identity, albeit in a more Han-centric context. The appropriation of Manchu "items" by the Han majority often ignored the history of this "items" as part of a oppressed group’s identity.
Now for long ones.
That still doesn't explain why - for example - the Chinese aren't allowed to keep China or the Italians aren't allowed to keep Italy. You seem to be saying that that's inherently objectionable and you haven't explained why you think that.
The 19th century gave birth to nationalism the idea that a nation was no longer just defined by its rulers but by ethnicity language and culture in this turbulent age which saw uprisings around the formation of a modern national identity (nation become group of shared culture), culture in this sense is a collective consciousness or shared understanding of a people.
Nationalism operate on the idea of linear hierarchy in which some cultures are more "superior". However cultures are not necessarily superior in a moral sense, but more developed in terms of Sittlichkeit the ability of individuals to recognize their universal principles. For example, a European culture that has developed strong democratic institutions might be seen as further along in terms of self-consciousness compared to one that is still in a more traditional-religious phase like the Arabic ones. But that doesn't make one culture "superior" in every respect it's just more developed in certain ways that contribute to the collective consciousness of humanity as it unfolds over time.
When two cultures interact, they don’t merely clash or merge into one homogenous form. Instead, they go through a dialectical process, which involves both preserving aspects of the original cultures and transforming them into something new or hybridized (transcend their original forms).
Italy is a great example of this because it's historical complexity. Having each its own culture and language. In the North regions was historically influenced by Germanic, this is due to the Lombards (Germanic Tribe), who invaded the Italian Peninsula in the 6th century and established their kingdom. After the fall of the Lombard kingdom and its replacement by the Holy Roman Empire, the subsequent decline of the empire led to the fragmentation of the north into city states like Milan and Venice, each developing its own distinct culture. In the south regions, its geographic location at the crossroads of the Mediterranean become a melting pot of Greek, Arabic, and Norman. The idea of a singular "Italian" identity is a long dialectical process.
So, your question why aren't the Chinese and Italians "allowed" to keep their respective nations based on their dominant ethnic groups? is not a "problem" but rather find it paradoxical because the very notion of "nation" is a constructed identity from culture that has evolved over time through dialectical processes eventually sublate into a higher synthesis. Nationalism seeks to define a nation by rigid markers of ethnicity, language, and culture, but no nation can fully define itself in isolation the idea cannot be static, instead nations are connected to each other and that interactions and conflicts between them are part of the broader historical development. This interactions and conflicts led to a synthesis that incorporates elements of both cultures while transcending their limitations. In this way, cultures can coexist, influence one another, and enrich the shared human experience, transcending the artificial boundaries that nationalism seek to create.