The question is very general, however normally your Internet activity can be monitored through your IP address. This can not only compromise your safety and privacy but it also can invite hackers. A...
The simple answer is that a LAN user (client) will not see all of the packets on the Internet; they will only see the packets for their own LAN segment.
If you want to be able monitoring internet activity you have to have a special network equipment. Customer level routers do not allow collecting all information passing through it. Usually they have...