What's the grammatical structure of 这是你第一次来中国吗？
Simply put. There is always S V O structure in Chinese. 

In this case, 这(this) is the S, 是(is) is the V, 你第一次来中国 (your first time coming to China) is the object phrase.

PS 你第一次来中国 = 你的第一次来中国. (The 的 in the first sentence got dropped)