Plan XYZ is a 'Supplemental Executive Retirement Plan' (SERP) which we
think is a 457(f) non-qualified plan. Participant F is retiring. The
Plan Sponsor is purchasing an annuity to fund Participant F's payout.

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Specific Questions:
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Q1-What tax form, if any should be used to report the purchase of the
annuity?
Q2-What tax form should be used to report the annuity payments?

Who owns the annuity? If the annuity is owned by the employer, I wouldn't think there was any tax consequence - just another asset of the employer. If the annuity is owned by the employee, or if it is set apart for the employee (not available to the employer's general creditors), it would probably be considered a payment that is taxable. Payments from a SERP are generally W-2 income.

457f plan benefits are included in the employees taxable income when the employee is no longer required to perform substantials services. 457 benefits are taxed as w-2 income when includible as taxable income.