Welcome to the USA! And, no, there are no stupid questions.
1) Savings accounts are not factored, or even listed in the CR. Checking accounts are not listed or factored into scores or report, but if an inquiry hits for opening that account, then it could affect your score (only very slightly, if even that).
2) The age of majority in the US is set by the states and is generally 18. Any younger and they cannot get their own card. However, you can add them as an authorized user. I know my wife was added to her fathers Citi Visa at the age of 14. Unfortunately, I hear that sometime next year FICO will no longer factor in AUs into the score. So, your kids can have that card but it won't help their score.
3) People thrive off hype. And if the credit industry sees that people want their scores, then anyone and everyone will offer it to you. It's all about the money.