Translation:His Chinese is as good as yours.
They all are basically prepositions. I.e. they come before whatever word goes with them, and the whole phrase is usually before the main verb (there are some special cases when preposition phrases can go behind the verb, e.g. 他住在北京 “he lives in Beijing,” but generally speaking that’s the exception).
没有 in comparisons patterns can also be explained in the same terms: 他的中文没有你的[中文]好. There may be grammarians who resist calling 没有 a preposition and would like to explain it as a verb, but I think from a learner’s perspective, it’s probably easiest to view it as a preposition in this construction.
Some slight corrections if I may:
他的中文想你的一样好 → 他的中文像你的一样好。(or 跟 would work too)
我是中国人和他是美国人 → 我是中国人，他是美国人。 (和 can only link nouns, not sentences. Where English uses “and” between sentences, you can usually just put them next to each other without a linking word in Chinese)
错啊: Not wrong, but sounds extremely blunt in Chinese, to the point where I would probably feel like the other speaker is picking a fight with me. 不对 sounds a little nicer.
你的中文不好想她的: Not entirely sure what you were trying to say here. Judging by the context probably something like “Your Chinese isn’t as good as hers?” In that case: 你的中文没有她的(中文)好。The formula is: X沒有Y Adj = X is not as Adj as Y. Or you could simply say: 她的中文比你的好（很多） ”Her Chinese is (much) better than yours.”)