If i'm part of a network can people see my computer files, or what i'm doing online?

my old roommate connected our computers with a network so that we could both be online at the same time, and use the printer. but i'm not very computer smart and when i looked at my internet security it says that there is a trusted computer, is that my roommates and can i erase it because it's on every location, like home, away and office, and even the new one i just made today. i don't know what i'm doing please help

plus i just set up a new internet service today and it says that i'm part of that network as well, so can other users of that internet provider see what i'm doing, and do i have to be connected to that network to be able to use the internet. i don't want people to be able to see stuff like when i look at my bank account and stuff.

If i'm part of a network can people see my computer files, or what i'm doing online?virus scan

I am assuming you are using Windows? If you stick a computer with Windows on it to any network with others Windows computers those other people will have to know an administrator password or password to an equivalent account to get into your computer remotely. I am a network administrator and I routinely look into machines for various reasons, its also called rooting the machine, or gaining root level access to the C: drive. If you have no Administrator password set then people can easily get in provided they are somewhat computer savvy. I suggest you set passwords for all accounts, especially the Administrator account if the computer is on a large network with other people that you do not know. If you are on a small home network or small LAN you have setup in a room then there really is no way for people to get in because they have no physical connection to your computer. If you are required to join the computer to a Windows Domain or someone has already done this to your computer, then the Administrator of that network has full access to your computer regardless of what passwords you set. If you have passwords set to get into your computer for all accounts and its your own computer and its not a member of a larger domain then your probably pretty safe. Make sure Windows Firewall is turned on and that will shut off all the ports that a hacker might try to use to gain access. If this is a small network hooked to a router and a high speed internet provider such as a cable modem or DSL, you are fairly safe because the router has a firewall, and also windows has a firewall too.