In English culture, when someone is giving other a surprise, he/she can call out with voice 'surprise!'.
Is there an equivalent in Chinese culture?
I can't recall any Chinese expressions used in the same way as calling out with 'Surprise!' in English. I guess the reason might be that Chinese Culture doesn't make Chinese people as playful as English Culture making its people.
We say something different from 'surprise!' in similar cases:
I bring a gift to a friend, before showing him/her the gift, I say: 猜我给你带来了什么？or 看我给你带来了什么？ Then show the gift, and after seeing his/her facial surprise expression, I say: 没想到吧？or 喜欢吗？He or she may say: 真没想到。or 我很喜欢。or 我太惊讶了！
We plan to throw a party for a friend's birthday, and one person leads the friend to a room where everybody else is hiding. When they come in, all the hiding people jump out together and say: 生日快乐！
In a classmates reunion party, we decide to invite the old flame of one of our classmates. Once that classmate arrives, we say to him/her: 你看谁来了？Then the old flame comes in to give him/her a surprise.
At a performance audition, the judge is pleased with an actor's performance. The judge may say: 你的表演很不错，但是你知道，其他的表演者也非常优秀。我知道你非常热爱表演，所以不论今天你是否被录取，我希望你一直坚持下去，不要放弃。Now the actor probably thinks he will not be picked. Then the judge says: 恭喜你，你被录取了！The actor is definitely surprised.
Many of them will actually use the English word, as weird as that sounds. This is true mostly with younger and more educated Chinese people. Here is a video of it actually being used in a very natural setting. Skip to 3:58. https://www.youtube.com/watch?v=VqUpsXF4Yu8
The very native Chinese word of 'Surprise!' which every Chinese can understand is "我操!", and you need to speak it aloud.
And to express the following mood after an surprise, you can say "真鸡巴XX" in which XX is an adjective, like "big, hard, hot, strong, sexual, pretty, good..."
So the whole sentence, for example, would be like that: "我操！ 真鸡巴硬"