Hi,
The news is encouraging. She brings it. The news she brings is encouraging.
The laptops are stylish. She brings them. The laptops she brings are very stylish. I hope that will help you understand which subject goes with which verb.
As for the other questions, they might be a little tricky. I can only tell you what I would say, but consider I am not a native speaker.
His pair of spectacles is broken. His pair of shorts is torn. ("pair" is singular)
His spectacles are broken. His shorts are torn. (They are plural, and this is the common way to say it. You really don't need to add "a pair")
Music and writing is where her talent lies (But I wouldn't be surprised to hear "are" instead, or even find myself saying it, although I think I would add "...are the places/areas where...").
Now you need to see if the native speakers agree, but remember sometimes subject-verb agreement can be tricky to native speakers too.