Invitations in a school bag often vanish. Then parents text late at night to ask when it starts. I would send one link with the invitation, so each parent answers once and you can count heads.
About the guest
The child's first name, and a parent's name and phone number. You need the number on the day, for pick-up and for emergencies.
About the day
Yes or no, brothers and sisters who might come along, and whether the parent stays or drops off. This sets how many party bags, plates and helping adults you need.
About safety
Allergies the host must act on, and who will collect the child. I ask for nothing else about health. A tick box records whether photos may be shared with other parents.
Who fills it and who reads it
Parents fill it in. The host reads the CSV. A parent's AI might ask "Will your child come to the party?" Then "Does your child have any allergies?" Then "Will you stay or drop off?" It shows the answers and sends them only after a yes. See agent-fillable forms.
A tip
Set the close date a few days before the party, so you can order food with a firm count. To ask what the family would enjoy before you book, use a party planning template. Planning a grown-up celebration? The wedding RSVP form also asks about meals and plus-ones. More ideas live in forms for events.
Questions
Who fills it in, the child or the parent?
The parent. The form asks for the child's first name and a parent's contact, and nothing more about the child beyond allergies the host must act on.
How do I know how many children to cater for?
Count the yes rows in the CSV, then add the siblings_coming column. Add the parents who plan to stay if you are also serving food to them.
Can I ask about gifts here?
The form has no gift question. You can put a short, kind note in the form description when you create it, such as no gifts please.