"What gifts should I not give to Chinese people?"
There is no "I" in the translated sentence, a better English sentence could be "What gifts should one not give Chinese people"
But this is translating English to Mandarin; so 我什么礼物不能送给中国人, might be more accurate. But by using the given translation, Duo is teaching us that "我" can be, and often is left out when it's understood in the sentence.
Omitting 我 is not entirely an implication of the subject but it makes this a common truth. We can do it similarly in English by saying "What gifts should not be given to Chinese people?" (Note: It is rarely expressed in Chinese in passive voice for such case, such as 什么礼物不能被送给中国人？which is grammatically correct but not acceptable in actual application.)
Yet the word order of your sentence is not correct. It should be (有)什么礼物(我)不能送给中国人？
Why is that?
I've heard that it's even preferred to put interrogative part near end of the question
In this order the direct object must go right after the verb rather than the indirect object. So
I might add that 中国人 are people who live in china and 华人 are chinese people
Yes, and in the mind of the Chinese, 外国人 is the opposite of 中国人, even if the Chinese person is traveling abroad.