Q: macbook pro mavericks  has been hacked

We just changed our service over to Cable and I am having some strange things happening on my macbook pro.  I run Mavericks.  I have a ms desktop that  is wired to the gateway (our modem is a netgear combined wifi and wireless  The mac is using wifi which I hook up with cables and remove them after.  It has been impossible to get into my gateway with any password I choose.  The problem I've been struggling with is that even when I do a factory reset and change the password. It does not work when I reenter the modem.    I've noticed a while ago that the mac is hooked up to a HP Jet printer that is not mine.  If I change it back to my SSID that is visible, after awhile it's right back to the hp printer. the printer is not password protected. I have a shared folder on the sign in page along with my sign-in folder.. When I go through the whole session again to get it online, it will actually sign in by itself. 

I am the only one who uses the mac.  Since we have cable I have not been able to use wifi on mac as it says I need to create one and can't locate a new airport utility...  So it automatically uses firewire, and DHCP, without a password or manual setup.  Even when I change the SSID, and there is no sign of my default SSID in the list of available networks, it finds the default one again, and it is instantly online. I've also had trouble keeping my phone and kindle to stay set up with wifi and password, but it doesn't stay on.  Now it's hard to keep it off WIFI. It seems to be on again after I turn it off.

I noted that some of my music in Itunes seems different, and set up differently.  Could they get my Itunes password?

after messing around trying to keep it on track, it stopped using the HP printer and started using an Iphone.  I quickly turned off PPPOE and dialup and then it promply returned to HP printer.  I completely turned off internet and shut down unplugged the mac.  Funny, now I have no problems with changing the password on PC and I can always access modem!!

so sorry for the long message, but I wanted to give the most info I could so there wouldn't be many additional questions.

Please help, I want my Mac back.