I know that you can sniff data which is transferred over wifi. Can you do that with broadband (wired)? And how can you secure the network, so nobody could sniff data both over wifi, and broadband?
It depends on the broadband technology being used. Generally, for most residential fiber and cable systems, about 32 or so houses share the same passive distribution network. As such, the information coming from the ISP goes to all 32 customers and the cable modem filters down the information for each customer. Using a hacked cable modem, it is possible to monitor all the traffic coming from the ISP, but it may or may not be encrypted depending on how the ISP is configured.
Similarly, traffic going to the ISP is moving in the wrong direction and can't be easily detected by other customers.