Why does Allah show the believers the horrors of the Hour? Did the Prophet divide the signs of the Hour into major and minor? And why doesn't Allah cause us to die so that we do not witness these horrors?

If the questioner means by "the terrors of the Hour" the major signs that appear before it (such as the emergence of the Dajjal and Gog and Magog), then the believers are exposed to these trials to purify them, raise their ranks, and expiate their sins. These trials only increase them in goodness and favor.

However, if he means the immense terrors that occur when the Hour is established, then the believers will be taken (their souls) before this; they will not witness it. Rather, only their souls will remain until after the descent of the Messiah, when a goodly breeze will blow and take their souls. Only the most wicked of people will remain, and the Hour will be established upon them. This will occur after the cessation of repentance and the rising of the sun from its west.

The Prophet, peace be upon him, did not categorize the signs of the Hour into major and minor. Rather, this is an exertion of effort (ijtihad) by scholars and a convention they adopted based on the meaning. What precedes the Hour by long periods and is customary they called minor, and what appears close to the establishment of the Hour and involves a breach of custom they called major.