What is the ruling of Islamic law regarding someone who feels the recurrence of moments and a fear of the end of their life after having prayed for death, and does this indicate that the end of their life is near?

As for past sins, you must repent and show remorse. What you are experiencing may be a psychological illness that necessitates consulting trustworthy doctors. Remembering death is prescribed to encourage obedience and asceticism, but pathological fear that hinders work and fills one with sorrow is not religiously مطلوب (mandated or desired). One should remove this fear by knowing that what is with Allah is better for the righteous, and that death is a comfort for the obedient believer. Everything is written and predetermined in advance, and "So when their term comes, they cannot remain behind for an hour, nor can they precede [it]." Pathological fear is of no benefit and does not avert destiny. Allah does not decree anything except for a profound wisdom; so, one should submit to Allah's decree and be content with His judgment and destiny, and know that Allah's choice for him is better than his own choice for himself, and that dying obedient to Allah brings immense good.