I'm going to jump in here because I want to see if I'm right! My take on the rules:
Question 1: Is this attack handled like a normal battle, i.e. do both sides get to roll on the CRT?
Yes. See 17.9, 2nd paragraph: "Resolve the combat normally..."
Question 2: Suppose the besieged army defeats the left behind force. Can the victorious force now try to intercept the other force that just left the siege?
No. It can't intercept into the initial space the besieging player moved into (17.9: "...the besieging player activates part of the besieging force and leaves the space..."), because at that point the non-phasing player was still besieged (11.1: "Armies inside a stronghold with enemy units in the same space may not intercept."). If the force that left the siege subsequently moves into another adjacent space, then an interception may be attempted.