From what I read, the police did no interviews of people who had been in the room where the shooting occurred. Most students have gone home. Eye witness testimony is not nearly as accurate as that taken several days after an event.
It is my understanding that immediate reports can be used as evidence in a trial whereas days later reports are considered hearsay. I am not a lawyer so please correct me if I’m wrong about that.
Either under the “present sense impression“ or “outcry“ exception to the hearsay rule.
You are wrong about that.
Witness reports of what they saw, what they smelled, what they heard (unless hearsay as below), etc., can be taken at any time and used as evidence. Timing of the report wouldn't generally have any impact on the report's weight as evidence unless it was a long time afterwards.
Hearsay is when somebody reports what someone said to them and that report is used to prove the truth of what was said. So if my friend John said to me that a light was red at the time of an accident, testimony by me that John told me the light was red would generally be inadmissible to prove that the light was actually red. That makes sense because I wouldn't have any personal knowledge of whether the light was red or not. They would have to go out and find John and get his direct testimony about the light, which would then be subject to cross examination.
Here, a witness report of what the perp said would not be hearsay. The testimony would be of the utterance itself, rather than the truth of what was uttered.