OSX Yosemite uses over 500mb daily, without me using it. And only the total data received shown in Activity Monitor - no detail in specific process

I don't think that the total displayed in Activity Monitor is the total you think it is. I think it is maybe just the last online action a process had. I noticed that while watching softwareupdate download data.

Just to be sure: Is automatic software update disabled? See System Preferences, AppStore. Also, do you have anything set to sync itself? iCloud (Photos and Co.?), AppStore, iTunes, stuff like that? For example, iTunes has its own "update settings" (see Preferences, last tab).

You can check in AppStore's "Updates" tab to see the recently installed updates.

Do you have control over the router? Maybe it has logs with timestamps so you could see if any other device used it or what else happened! Because you said that the Internet is expensive, it could be that someone else is using it.

I assume you have the WiFi secured and it is not public? Use the strongest encryption your router offers and I would change the password, just to be sure.

May be it's the software that comes with the wifi router / 3G - have you installed anything for that?

Is this happening since beginning or started it later?

Also, you could ask your provider for logs or more information about this traffic.

Good Luck!