1. It's "has" because it refers to the singular 'spectrum', and not to the plural 'Indians'.
2. By aforesaid reason, we, students endeavored to notice really malaria is under-diagnosed in our country by studying controls and cases.
Your main mistake is writing a sentence that no-one would ever speak. Keep it simple. I would express it as something like, " For this reason, [or "Because of this,"] we students studied controls and cases, and noticed [or "concluded"] that malaria is under-diagnosed in this country".
Student or Learner