What are the verdicts of law suits in Law & Order Special Victim Unit?

I started watching Law & Order Special Victim Unit from season 1. I noticed there is a mini plot next to the major story line in each episode, and the mini plot normally involves a member of SVU goes to court and testify against a suspect.

E.g.:

1. In episode one, Payback, an inexperienced detective from SVU goes to court and testify again a suspect that sexually harassed a woman who has died. The defence attorney comes up to this detective and asks for the terminology for this type of sexual crime. It is not revealed whether this man is convicted.
2. In episode two, A single life, the African American detective goes to court and testify against a father who allows sexually explicit Japanese cartoon in his house so that this father's son (13 years old) commits a rape later. No verdict is delivered.
3. In episode three, Or Just Look like one, a detective goes to court and testify against another sex offender and gets into a competition with the defence a lawyer over some terminology. No verdict is delivered.

Why?