Q. 1. What is an Apostolic Blessing? I never heard of such a blessing.
A. 1. An "Apostolic Blessing" or a "Papal Blessing" is a blessing bestowed by the Pope, either directly or by delegation through others. Bishops are authorized to grant it three times a year and any priest can do so for the dying.
According to the "Rituale Romanum," the Rite of the Apostolic Blessing with Plenary Indulgence should be administered at the hour of death. It is given after the reception of the last Sacraments (Confession / Communion), to those who desire it while still rational and conscious. It may likewise be granted to anyone who has given any indication of such desire, or who has seemed contrite before becoming unconscious or irrational. But it must be denied absolutely to the excommunicated, the impenitent, or those who die in patent mortal sin.
Please consult "The Enchiridion Of Indulgences; NORMS AND GRANTS, Authorized English Edition, Issued by the Sacred Apostolic Penitentiary, 1968; Formatted into electronic text, June 2, 1998." Herein you will read...
"To the faithful in danger of death, who cannot be assisted by a priest to bring them the sacraments and impart the Apostolic Blessing with its plenary indulgence (see can. 468, 2 of Code of Canon Law), Holy Mother Church nevertheless grants a plenary indulgence to be acquired at the point of death, provided they are properly disposed and have been in the habit of reciting some prayers during their lifetime. The use of a crucifix or a cross to gain this indulgence is praiseworthy.
The condition: provided they have been in the habit of reciting some prayers during their lifetime supplies in such cases for the three usual conditions required for the gaining of a plenary indulgence.
The plenary indulgence at the point of death can be acquired by the faithful, even if they have already obtained another plenary indulgence on the same day.
The above grant is taken from the Apostolic Constitution The Doctrine of Indulgences, Norm 18."