The Succubus states that's she's mad so take this also as I know I won't be mad after I leave. But why does she give you the sword? Is it a reward for not killing her etc?
Yes, she rewards you for not killing her.
Witcher are known for their "no payment, no service" attitude.
She also gives him some hair (a trophy), so the guards think she was killed, so she would not be pursued.