Does Allah forgive the sin of insulting fate after sincere repentance, knowing that the one who committed the sin was constant in prayer and was afflicted with failure in his studies, and is this sin considered Shirk, which Allah does not forgive?

If cursing religion and fate was uttered by you verbally, then it is an apostasy from Islam. As for abandoning prayer out of laziness, the preponderant opinion is that it is disbelief.

No matter how great the sin, Allah accepts sincere repentance and transforms evil deeds into good deeds for whoever repents sincerely, as Allah Almighty says: (Indeed, Allah does not forgive association with Him, but He forgives what is less than that for whom He wills). This applies to those who have not repented from shirk (polytheism). As for one who repents before death, Allah accepts from him.

Sincere repentance demolishes the sins that preceded it, and Islam demolishes what was before it, whether the disbelief was original or apostasy followed by repentance, as Allah Almighty says: (Say, "O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.")