Do I need to let parents sign a contract in my show that challenges kids to do stuff?

Yes, you need liability releases from the contestants and their parents.

You need to get a lawyer for your show, for this and many other things. I do this sort of work. First, you should not have any child doing anything that is even slightly risky or dangerous. The challenges should not be physically risky or mentally or emotionally harmful. If a child is harmed on such a show, there is no waiver that will keep the child from suing when he or she turns 18, even if the parents did sign. In our society and in law, children are protected and any action that entices a child to engage in a potential or likely injurious situation is also probably criminal. You really do need a lawyer working with you in the early phases of planning your show.

Absolutely, you need a release that permits the children to participate in the activity, that addresses liability issues, that provides notice that the event will be recorded, copied, and distributed (when, where, how, and for how long), that grants you the right to edit segments together and/or leave out segments, that allows you to promote and publicize the program(s) including the children's names and likenesses, that states the amount the children will be paid or otherwise recompensed for their appearance, and, if you are providing gifts or prizes, that the children and their parents are responsible for any tax liability. If your kids are represented by an agent, you will need a release with additional information, including who gets paid and when. If you're talking about major amounts of money that the kids might win, you may also have to deal with trust issues (Jackie Cooper trusts for minors appearing in the media).