Do the curses that come to mind against God when remembering an affliction or hardship, without uttering them, count as inner monologue, and is repentance required for them?

As long as these are whispers that have not been spoken, they are from the thoughts within oneself, and the servant is not held accountable for them. Therefore, there is no need for seeking forgiveness specifically for them. However, seeking forgiveness (istighfar) is commendable in general and is of great benefit; it is among the greatest good deeds. So, whoever feels a shortcoming should resort to affirming the Oneness of God (Tawhid) and seeking forgiveness, for in them lies healing if done with sincerity and devotion.