Hi @Martje1
1) I'm pretty sure if you have multiple accounts, you can already choose which account you want to log in to on the Chromecast without using your phone. You have to make sure all the relevant accounts are added to the Chromecast, but once they are, you shouldn't need your phone to change/choose accounts.
2) Also, the family account is something I believe they already planned and said is coming. But on the "Help" topics, for that question all they say is "Stay tuned for more details on upcoming Stadia features."
3) Sorry, can't help with this one! I don't know any games for small kids.