Should I apologize if a kid gets hurt?

Express care, absolutely: "I'm so sorry this happened" is human and, in many states, expressions of sympathy are protected from being used as admissions. What you avoid is assigning fault or promising payment, which are different sentences entirely.

Do I have to report every scraped knee to my insurance?

Ask your agent where they want the line, and when in doubt, report. An incident report is not a claim, it costs nothing, and it protects coverage if a minor thing grows a story later.

What if the parents were not watching their kid?

Your documentation notes the facts, including supervision, without editorializing. The supervision clause exists for exactly this, and the person who weighs it is your insurer, not you at the event.

Can I be sued even with a signed waiver and insurance?

Anyone can file anything, which is precisely what the insurance is for: the policy typically covers defense, not just payouts. The waiver, the briefing, and your documentation are what make that defense strong.

What happens if a kid gets hurt at my event?

Your response in the first ten minutes matters more than anything in the contract. Stop the activity, get the child to their parent, help with first aid, and be a calm human first. Then document what happened, notify your insurer the same day, and never negotiate or admit fault directly. The waiver, the insurance, and the rules briefing all exist for this moment, and so does this plan.

In the moment

Stop the foam and the music. The crew lead calls it without hesitation. Nothing about the party matters more, and every parent watching is learning who you are.
Get the child to their parent, and help. Your crew supports with the first aid kit and clear heads. For anything beyond a scrape, encourage medical attention and never talk anyone out of calling for help. Kindness and competence here are also, incidentally, the best legal posture there is.
Say human things, not liability things. "I'm so sorry this happened, let's take care of them" is right. "It's our fault, we'll cover everything" is a promise you're not authorized to make, because coverage decisions belong to your insurer. Care without confession.
Resume or wrap based on the host's read and the injury's weight. A scraped knee and a wave from mom, the party goes on. Anything serious, the crew lead and host decide together, and erring toward wrapping up is never wrong.

Within 24 hours

Write it down while it's fresh. Time, what happened, where, who saw it, what was said, what care was given, surface conditions, and photos of the area. The crew lead's plain, factual account, same day. Memory is the first thing a dispute erodes.
Notify your insurer even if it seems minor. Policies require prompt notice, and late reporting is a classic way coverage gets complicated. Reporting an incident is routine and costs nothing. A claim may never come, and now you're covered if it does.
Check in with the family. A call the next day asking how the child is doing is decent, and decency is remembered. Stay with care, not fault or money, and if the conversation turns to costs or compensation, that's the insurer's lane: "let me connect you with our insurance so this gets handled properly."
Don't post, don't speculate, don't discuss it with other clients. The incident is between you, the family, and the insurer.

Before any of this ever happens

The response plan is the last layer. The layers in front of it:

The rules briefing, every party, out loud. Thirty seconds from the crew lead before the foam starts: no diving, walk in the foam, glasses off, littles to the edges. It prevents injuries and it documents that rules were given.
The waiver and supervision clause, signed. The host has acknowledged the activity's nature and that adult supervision stays with the party's adults.
A real first aid kit in the truck, checked seasonally, and a crew lead who knows where it is.
The insurer's claim number saved in your phone, because looking it up is not a day-of task.
General liability in force. The policy is the plan for the version of this day that goes badly. Operating without it means self-insuring against the worst thing that can happen at your events.

The line to remember

Handle the child like a parent, the paperwork like a professional, and the money like it's your insurer's conversation, because it is.

We're operators sharing what we've learned, and laws vary by state. Have a local attorney read anything you plan to rely on, and direct incident-specific questions to your insurer and counsel.