may be you doubt why use hit to describe "turn on" i answer you tomorrow

Both are correct. You can also say 把燈打開 幫我開個燈好嗎？Can you turn on the light for me?

Generally speaking, they both are correct. Strictly speaking, they are a little different. let me explain, first, "打" is action, "开" is state of things. 开灯：1.Describe the state of light, ok, the light is on. But when you write an article, you need use past tense. Example: 灯开着(了)。 2.Imperative sentence. And in our daily life, we usually add modal particle at the end of sentence, and make the sentence more polite. Example: 小明说：“这里好黑啊。”= it‘s too dark here. 小红说：“开灯吧。” 打开灯：Emphasis on action. Example: 请打开灯。or 请把灯打开。 By the way, many things can use this word, 打开电视（TV）, 打开冰箱（refrigerator）, 打开箱子（box）, 打开书本（book）…… and you also can say 翻开书本, “翻” is an action too, 翻 describes more detailedly than 打。

Both are right.

Both them are correct, the first one is more common.