1)
How could Asa and his father Aviyam have the same mother?
1.
Radak: The mother of Asa's father is called his mother, just like "va'Tavonah El Re'u'el Avihen" (Shemos 2:18; really, he was their grandfather). It mentions Asa's grandmother, because she served idolatry, like it says in verse 13, and even so Asa did Hashem's will, and was not drawn after her 1 .
2.
Ralbag: She is called Asa's mother because she raised him - and even so, he was not drawn after her.
