Is the torment mentioned in the verse (And whoever does that aggressively and unjustly, We will soon cast him into a Fire) specific only to one who kills his brother, or does it include the one who commits suicide? And is there a suicide or self-killing for which Allah does not punish the perpetrator because it is not an act of injustice and aggression?

The Almighty's saying: "And do not kill yourselves" (Qur'an 4:29) includes the prohibition of a person killing themselves and people killing one another. It has been interpreted in five ways:

1. A clear prohibition against suicide. 2. Do not kill one another. 3. Do not burden yourselves with an act that might lead to your demise, as Amr ibn al-Aas did when he prayed while in a state of major ritual impurity (janabah) fearing perishing from the cold. 4. Do not neglect your own well-being, for whoever neglects it is as if they have killed themselves. 5. Do not kill them (your souls) by committing sins.

As for the existence of suicide without aggression or injustice, the answer is yes. A person might do something that leads to their destruction unintentionally, like someone who drinks poison thinking it is food. This is killing oneself by mistake. The threat in the verse is restricted to aggression and injustice to exclude acts of forgetfulness and error.