Is it permissible, Islamically, to entrust one's will and life to God "as each of us understands Him," and to admit one's errors to God, to oneself, and to another person?

There is no issue with the two aforementioned phrases. The first means entrusting the matter to Allah Almighty, in accordance with His saying: "Say, 'Indeed, my prayer, my rites of sacrifice, my living and my dying are for Allah, Lord of the worlds'," and His saying: "And you do not will except that Allah wills." As for the second, it means acknowledging error and transgression before Allah Almighty, as in His saying: "They said, 'Our Lord, we have wronged ourselves, and if You do not forgive us and have mercy upon us, we will surely be among the losers'." Acknowledging one's own faults is essential, whereas acknowledging them to others is fundamentally based on concealment, unless it serves a benefit for the one confessing or for people, as happened with the man who killed ninety-nine souls.