Will Christians who are alive when the trumpet sounds have to die first?

No, believers alive at the trumpet will not die first; they will be changed in a moment, in the twinkling of an eye, at the last trump. The dead are raised incorruptible, while the living are changed from corruption to incorruption directly.

Les explains that this event is not the Second Coming; it has no prophetic sign and could happen at any day or year. At the last trump, the dead are raised incorruptible, and those who are alive and remain will not die and be resurrected but will be changed. In a split second, this corruptible puts on incorruption and this mortal puts on immortality, losing the flesh-and-blood concept and becoming flesh and bone activated by the Spirit.

1 Corinthians 15:51

Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed,

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What happens to Christians who are still alive when the rapture occurs?

Christians alive at the rapture will not die and be resurrected; instead they will be changed in a moment, in the twinkling of an eye, at the last trumpet. Their corruptible body puts on incorruption, and their mortal body puts on immortality, becoming flesh and bone activated by the Spirit.