Is there a way to sign your account out of your console without actually being on it?

Actually, If your dad is signed in on your console, you can sign on your account also and you will have gold. (if you're in his xbox family) Any other xbox family member can be signed on his home xbox without his account being signed on. Your dad can only play on one console at a time but can actually be signed on two.

The only way they can make purchases is if they are actually using your account which they shouldn't be. If they can't access your account without you signing in, then they can't make purchases.

You can go here to remove your account from all 360 consoles. This will require that your account be redownloaded before being used (even on your own console).
live.xbox.com/.../Protection

Hi,

It would seem that there's no way to "sign out" of Skype on the Xbox One without actually signing out of your account on the console.

The support page here currently lists all of the troubleshooting for the application as well as features.

Hey ayyubahmed

Thank you for taking the time to post this on the Xbox Forums. We understand that you are currently inquiring about being able to sign-in or out on your account though the Xbox app on your mobile device.

At this time, there is no way to remotely sign out of your account on your console by using any other device besides your console. If you sign into another console while you are signed in on one console, the most recent sign in will kick out your account
on the other console.

I hope this was able to clarify any confusion this might have caused.

Nothing can be transferred between accounts, but if you set the console as your Home console, he can access the game without your account being signed in.