Q4. How can prayer change God's mind without conflicting with the
doctrine of the Immutability of God? Can God answer a prayer for
something outside of the scope of his will?
1st, we can not measured God's mind. God's will is not our will, God's thoughts is not our thoughts and God's heart is not our heart. We can not think God as like us, human!
If God's change of plan or mind (and if we aware God's action), it will not conflict with any doctrine; as God answer prayer with Love. Love is above all; that is the basic ingredients for all answered prayer. God's love rules.
God can answer all kind of prayers; God is the creator of this universe, nothing is to hard for HIM. God is sovereign; we can not put ourself in the level of GOD's sovereignity.
The questions is "Are we ready for that prayer? Are we ready for HIS answer?".
Nothing is to hard or impossible for God.