There is no perfect answer, as any given file could be protected in a number of different ways. You need a method that gets around detection, logs, and warnings, and that can range from sending an email to booting a different operating system. The only real way is to know how the action is traced in the first place.
The only way to be certain of whether a file was copied or not is to have a file monitoring system in place before the copy is made. Without such a system, you can use native resources to try and guess whether or not a copy was made, but you won’t know for sure. Truly knowing requires preemptive measures or guesswork.
There are many ways that an employer can see if and when you copy files from a work computer. Monitoring systems and computer logs provide the information and can even send off alerts. But, your employer will only be able to track activity if they set up the ability to do so before you make your copy.
Technically, a router can be used to track internet history. But, the burden of knowledge and the sheer difficulty of the task make it impossible for most households. In fact, professional IT researchers would struggle to track internet history through a consumer router.
Yes. If you connect to Wi-Fi run by the school, they can see your internet activity. In fact, they have to be able to see your internet activity in order for the connection to work. How much they can see and what they do with the information varies widely from school to school.
If you’re using a company computer in the workplace, your employer can see your browsing history. If you’re using a work computer or company network from home, they might see your browsing history. If you’re using your own computer at home, not connected to the company in any way, they can’t see it.
The short answer is no. Although your ISP might have access to your browsing history, it will not be listed on your bill. Still, you should be aware that some information can get to your bills. For example, if you are subscribed to particular web content, your credit card bill might display this information.