"Ask people which of these four crosses they like best".
Q1. I wonder if the sentence above can be considered as a garden path sentence. It is difficult for me to parse, whether a) Ask people which of these four crosses / they like best, or b) Ask people / which of these four crosses they like best.
No, it isn't a garden path sentence. The sentence is perfectly straightforward. It is an imperative. "Ask" is the verb of the main clause. "People" is the indirect object. The direct object of "ask" is the embedded question "which of these four crosses they like best." There is no other way to parse the sentence.
Q2. Do native speakears usually use such complex sentence in their speaking or informal writing?
Yes, we do. There is nothing complicated about the sentence at all. If you have difficulty understanding it or parsing it, please try to indicate what confuses you about it. Phrased with a direct question rather than an embedded question, the sentence reads: "Ask people, 'Which of these four crosses do you like best?'"