Very close. "I'm at school" - This is an answer to "where are you?" or "What are you doing now?". It implies you are a student there. Similar to saying "I'm at work". If you aren't a student there, you would probably say "I'm at the school" (similar to "I'm at the bank). In both cases, you could be inside or outside. "I'm in school" - You're enrolled in school and taking classes. You could still have a job. If you are ONLY in school and have no job, you would usually say "I'm in school full-time". "I'm in the school" - You're in the school building. You don't need to be a student, you could be visiting a school and say this

I'm in school: I'm attending school (I'm a student) I'm in the school: I'm inside the school, I want to give you my location I'm at school: this is what I'm doing right now. I'm at school, doing my thing at school. In/at can be interchangeable sometimes but IN emphasizes the LOCATION, AT emphasizes the purpose/the reason why you're there. For example if I say "I'm at the gym" I'm probably working out, if I say "I'm at school" I'm probably attending class, studying etc..

That's exactly right!

Я сейчас в школе - I am at school now. Я сейчас внутри здания школы - I am in school now. The добавляется когда идёт упоминание о конкретной школе а не вообще о школе, например о школе в которой ты учишься.

at school