Hi,
Your sentences mostly work well for a casual, conversational tone. Here are a few light edits for flow and clarity:
1. He’s too stressed. Seems like he doesn’t have time for anything but work. (Slightly more casual without “It seems like”)
2. He’s so stressed — looks like all he does is work. (“And nothing else” is a bit redundant)
3. Students know that teachers do more than just teach. (This one’s perfect as is)
4. He was a really curious kid and took a lot of courses outside school too. (“Outside of” is fine, but “outside school” is more concise)
5. This kid did more than just homework and playing outside. (Cleaner and more natural)
6. Many people don’t do anything else in their free time except watch TV and scroll through social media. (Added “media” to complete the thought)