Translation:Maria is a foreigner.
Gaijin seems like a shortened form of gaigokujin, but it is not. Its not like "Arigatogozaimasu" vs "Arigato". Where the shorter version has the same meaning just less formal/less casual. Gaijin and Gaigokujin carry different meanings and are not related to one another the same way other short/long forms are, and should not be thought of as short/long versions of one another.
It's kinda like the difference between "outsider" and "person from abroad" in connotation. The former has a negative connotation (like gaijin, literally "outside person") while the latter is more neutral (like gaikokujin, "outside country person"). Part of it is attributing the "outsideness" to the country of origin, not specifically the person.
Actually, even though grammatically I can see where you're coming from, in Japan it is often used as a shortened version and not meant to be rude by most Japanese but it highly depends on the context. I've noticed that young casual Japanese (teen-young adults) usually say gaijin san mostly but if you're doing something official in a government building or business they'll pretty much always say gaikokujin. Gaijin is not exclusively a slur but it certainly can be depending on tone and context.
Yes! It does to me too, and I think this gets at something deep.
This is a great illustration of the limitations on romanization. It's tempting to see that we romanize が as "ga" and wrongly think that it makes the same sound. If you pronouce it as "ga" as in English, Japanese will usually understand you, but the two sounds don't exactly correspond, and there is also a range of pronunciation of these sounds.
I've found that most of the time, が is much softer than the English hard "g" sound. In many cases it is pronounced a little more like an "ng" sound, like at the end of "sing". We don't use this sound in English as an initial consonant in words, so it can be hard for us to hear or understand it in this way, but with time, and exposure to enough examples of this, you'll get it.
It's important too, if you want to understand native speakers, as there are people who pronounce this consonant even softer than in this recording, especially in certain contexts or words.
It's an example of a Japanese dialect difference, generally East-West and more recently young-old, called Bidakuon / 鼻濁音. Super interesting and in-depth link here: https://web.archive.org/web/20180628233419/http://ysjapanese.wp-x.jp/2015/10/bidakuon/
外国人 is a noun, though, and you used an adjective. Especially given the cultural implications of words used for people from other countries, that can matter. It could be as big a difference as "Maria is foreign" vs. "Maria is an immigrant" in the US -- given how a lot of people feel about illegal immigration, that might completely change the tone of the statement.
(You're are probably making a joke, but I'll explain anyway.)
She's not referring to China the country itself as a western concept so much as the name given to it as western. The Chinese don't call their nation "china"; that name came from a Portugese word most likely referencing the Qin or "Ching" Dynasty of the country's history. Actual chinese folk themselves say 中国/"Zhōng-guó".