1)
Why did Hashem accept his prayer?
1.
Malbim: (a) His prayer aroused and mentioned his merits. (b) His tears aroused mercy. After he fixed the internal, the external enemies (illness and Melech Ashur) departed.
2)
To what days is Hashem adding?
1.
Radak (Melachim II, 20:6, citing Yevamos 49b) #1: He added back what was initially allotted for him, and it would have been deducted due to his sin (of not marrying) 1 .
2.
Radak (Melachim II, 20:6 citing Yevamos 49b) #2: He added to what was initially allotted for him.
1
Radak: I explained this in Sefer Shmuel. Refer to Shmuel I, 26:10:5:1 and the note there.