Dear C.,
I think your question was about invitations, but like the other posters I am also wondering about this type of a party at a school. But, re: invites, I don't think those are necessary since the activities will take place during the course of a typical school day.
I think it is awesome that your kids' school permits parents to come in and teach a lesson alongside staff. Cooking can be fun and educational.
You will need to check with staff re: policy of bringing in outside food. And check to make sure there are no food allergies and/or health or religious exceptions to ingredients that you plan to use. Some schools don't permit sweet treats for birthdays. Others have strict restrictions due to food allergies.
But, I think fresh lemonade and fresh fruit with whipped topping sounds great.
I would encourage you to reconsider the rest of the plan though. I think a simpler "Cooking Class with the Birthday Boy" is perfect. Kids really enjoy having their parents in class and simply being there and doing a simple, healthy cooking activity is plenty.
In schools, kids do notice what other kids "get" and the schools really do want to be equitable. I would gather that not all kids at the school could afford to have a parent bring in games, pinatas and gift bags for each child.
But, having a parent in class is super cool for a kid. So, I think you could come in and do the cooking class and the kids get to have fun with you and your son gets to be the star for an hour.
Other parents could also do this for birthdays. Like, bring in a favorite book to read to the class, then donate the book. Or bring in a blank canvas and have the kids paint, then donate the completed project. Or come and cut up fruit and pass out fruit salad. Once I brought in a photo of each child (taken the week prior) and scrapbook supplies and each child decorated a scrapbook page, then my daughter donated the scrapbook to the school.
Of course, clear this with the staff ahead of time! Teachers have lessons plans made the week prior, typically.
The classmates will get to enjoy the results of their labors and your child gets to have a parent in the room, which is a big thrill for a kid. There is no need for extra games, prizes, pinatas and send-home treats in a school setting. Having a parent there is a big enough treat! If you have the time and can afford a home party, then you can do the rest of the stuff at that time.
Have fun!