I don't want my son watching YouTube (he keeps redownloading it) on Chromecast with Google TV. Is there any way to limit what apps can be downloaded or used (with a pw or pin, perhaps) without having to create a new account for him? I can't find the answer online. Thanks.
I didn't understand what you asked for clearly. However, if you meant you want to restrict Using Google Play Store or Just the YouTube on your any device (Smartphone/tab), you can do that by using installing App locking app from Play Store. If you do that make sure you locked the settings+play store+that locker app. Otherwise, by uninstalling that app your son will get control back. I use Bitdefender Mobile Security (Paid), it has features of locking any app with PIN/SmartLock. You can use any other security apps. Search Google for top ranked security apps and check if they have your desired features or not. Try to use the paid version of any top ranked one. Please, consider ignoring my poor English.
You can create a kid's profile that does not use an account. Head over to the top right of the screen to create one.