You need to set boundaries. Tell him that you understand he needs support, but you have your own exams to focus on, too. If every call revolves around his worries, with no room for your thoughts or needs, that's emotionally draining. You’re allowed to put yourself and your goals first. The HSC is a big deal for you, too
Regarding the fake papers, ask him about it calmly and directly. If it turns out to be true, that’s a serious breach of trust. It shows a lack of respect, which could be a red flag in your relationship.
You deserve a partner who respects your time, emotions, and goals, not just someone who turns to you when it’s convenient for them. If you’re not getting that, maybe it’s time to re-evaluate whether this relationship is giving you what you need.