“Then Abraham fell on his face and laughed.” It is interesting that the Bible does not tell us why Abraham laughed. Joy? Doubt? Surprise? Or maybe a mixture of emotions… In any case, it is interesting that God did not question Abraham about it as He did Sarah even though they both laughed to themselves, not out loud (Gen. 18:12).
“him who is 100.” The Hebrew is idiomatic: “to the son of 100 years.” The same is said of Sarah: “a daughter of 90 years.”