england-and-wales
First your ask:
But what about other people? About 400 people were injured as a result of the panic that ensued -- a reasonable person can anticipate this, so it seems like there could be charges for recklessness. Would it be a count for each injured person?
A defendant can be liable for panic-induced injuries to bystanders if those injuries result from a reasonably foreseeable escape attempt triggered by the defendant’s conduct. For example:
In R v Roberts, the victim jumped out of a moving car following unwanted sexual advances. The defendant was held liable for assault occasioning actual bodily harm despite the direct harm being caused by the victim's actions.
Therefore, if people are trampled or hurt while fleeing, and that panic was a natural and foreseeable reaction to indiscriminate gunfire, the shooter could, in principle, face one count per injured person, assuming sufficient causal connection.
This won't apply in every case. Lord Justice Stephenson (in the judgement of the aforementioned case) stated that if the victim’s act was sufficiently unreasonable, then it would be considered to be an independent voluntary act. Therefore, each case would require individual analysis.
Ultimately, in the same way that property damage is probably not worth considering in a case like this, the same principle likely applies here. There are far easier and more severe charges that can be established.
You also ask:
On top of criminal charges, could there also be a lawsuit for pain and suffering by the attendees (maybe a class action to simplify the proceedings)?
Each injured person has a separate course of action and these will not be aggregated automatically (although they can be). Given the indirect nature of the injuries in question, we look to the principles governing the tort of negligence. This requires us to establish that the defendant breached a legal duty of care, which caused the ensuing harm.
Again, on a case-by-case basis, this would require looking into the foreseeability of the harm and whether the shooter legally caused the harm to that individual (legal causation is not the same as factual causation). An individual who was trampled in the panic, would likely have a strong case. On the other hand, if several people were run over by a driver trying to escape by driving through the crowd, they would have a weaker case against the shooter and may want to consider proceedings against the driver instead.