MacOS – How to measure, that how much data of internet I used on MAC for a certain period of time

First, connect one of the Ethernet ports of the 2Wire Gateway to the WAN port of the Time Capsule and turn both devices on, and disable wireless on the 2Wire. Your Time Capsule settings should not be changed from what they were when you had things working with your cable modem. If you've changed them, change them back now.

Then, on the 2Wire Gateway, in the "LAN" section:

1. Enable DMZ for the Time Capsule connection
2. Turn off the firewall for the Time Capsule connection
3. Set the Address Assignment for the Time Capsule connection to "public"
4. Set the WAN IP Mapping for the Time Capsule connection to "Router WAN IP address"

Then cycle power on the Time Capsule. The Time Capsule will now control everything just like it did when it was connected directly to your cable modem. Any wired Ethernet connections you add should be connected to the Time Capsule, not the 2Wire Gateway.

FYI, this works for any router or access point, not just the Time Capsule.

Don't overlook "the parent app".

It turns on the logging of safari using parental controls. Sets the normal time limits when the mac can be on and off.

Then it communicates to the children "the rules" and what happens when the parent determines that they have been broken. Why spend money or time on a more controlling solution if you can ensure they don't cover their tracks and will be caught if they stray.

Technically, managing this on the router is easier than on the Mac using the default Apple tools.

Apple has implemented timed access across the airport line, so fire up Airport Utility and set the times when you want access to the Internet.

You can set up default timed rules as well as specific policies for specific devices.

If you really want things to be controlled locally on the OS, turn on time limits under Parental Control under system preferences for each user account:

And then prevent apps that you don't explicitly want them to use.

I believe Firefox (if installed) defaults to on - so do review each and every app in the list. Your children can come to you as the administrator and you can over-rule these restrictions with your password - so this is the unattended default situation and you can grant them extra leeway with your password when needed.