1A. Was the precise day for the organization of the church revealed to Joseph Smith, along with the name?

Yes,
The name given by "divine revelation" was, the Church of Christ.

Four years later on April 3, 1830, the name was changed to, The Church of the Latter-day Saints.

Then four years later, in April of 1834, the name was again changed to, Church of Jesus Christ Of Latter-day Saints.

Doesn't it seem strange that it took eight years and three revelations to name the "true church"?
Changes in Mormonism

History of the Church p. 63

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