Digital Purchases on 360 console with multiple gold accounts

When you purchase content it's tied to the gamertag that purchased it as well as the console it was purchased on. The console license allows all profiles on the console to access the content. So yes, if account A purchases a game, account B can access it.
Account A can redownload and use the game on any console as long as it's connected to Live.

You can only designate 1 console as the Home Gold console. Anybody in your home who logs onto that specific console gets gold benefits even if they are silver. As a gold member, any Xbox One you log into has gold benefits as long as you're logged in. In
your own home, you would need 1 gold account for every 2 Xbox Ones. Designate the One the non primary user has as the Home console. That way they can have a silver account, but gold benefits. Make all digital purchases on that console. The primary user has
the non Home console, but access to all digital purchases & gold benefits. As of now, it doesn't carry to the 360, so multiple console owners are kinda getting shafted. I would think tthey'd adopt the same plan eventually.

No. If the console in your kid's room is set as the Home console, he can log in with his silver account & get gold benefits. The person with the gold account gets gold benefit no matter what system they're on, as well as access to all digital purchases.
You aren't signing in with the same account. On the 360 side, you are as of now getting shafted.

there is a special family plans if u wanna run multiple accounts in a single household

The Family plan has been discontinued since 2013.

Instead, the owner of a Gold membership can sign into the Xbox One console the family uses, and set that console as their "Home Console".

If the Gold owner account goes to the console's settings and under "Personalization" sets that console as their "Home Console", everyone playing on that console will benefit from the Gold owner's Gold membership (and is also able to play that person's digital
games).

This does not work for Xbox 360 consoles, however.

If you purchased the games digitally you can then download them to the all digital console as long as you’re signed in to the same profile that purchased them. Just remember you can’t be signed in on multiple consoles under one account.