If the annuity payment is fixed, what happens if the trust makes more money than that?

Any excess earnings in the trust belong to the beneficiaries, the annuitant’s heirs. It may be paid to them at any time, or held until the annuitant’s death.

What happens to the money left in the trust after my death?

Everything left in the trust at the annuitant’s death goes to the beneficiaries.  It may be paid out to them immediately, or paid over some pre-specified time frame.