I am not sure about the significance of the 49th and 100th days. But I have heard an explanation for waiting for 7 days before making an offering to the bhukkhus and giving merits (pattidana) for the diseased person.
As we know, when a person’s physical body dies, the mental body (gandhabba) comes out if the kammic energy for the human bhava has not run out. Then that gandhabba has to wait for many years before a suitable womb becomes available. During this time, it is possible for the gandhabba to receive merits form the relatives.
However, when that gandhabba comes out of the dead body, he becomes disoriented for several days (let us assume it is a “he”). First there is no realization that one has lost the “solid body”. Contrary to what we believe, one may not feel much pain at death. Sometime back, I watched a youtube video of a rebirth story of a person who died in an automobile accident. The reborn child says he remembers his car getting hit by a large truck, and that next moment he was watching the scene of the accident from above. He said he did not feel any pain. Maybe he died instantly.
The following is not from his story, but is a generic description given by Waharaka Thero. A “new gandhbba” tries to talk to the humans around and of course they are not aware of him. If he wants to get somewhere, he gets there instantly. So, most people who die of accidents just go home instantly to their surprise. Then he tries to get a drink, but of course there are no sold hands to hold a cup. So, it is a confusing time period for the new gandhabba. But other gandhabbas teach him how to function in that world, called “para loka” by the Buddha. It exists “side-by-side” with our human world, but we cannot see that world.
The bottom line here is that it takes the new gandhabba about seven days to settle down in his new world. Until then his mind is too agitated to receive any merits. That is the reason for waiting for 7 days before trying to “give merits” or pattidana. For a discussion on pattidana, see, “Transfer of Merits (Pattidāna) – How Does it Happen?“.