Can the websites I use be tracked through wifi?

Well, yes , it is possible to track what someone is doing using the wireless router. Weather your parents track you or not is a completly different story. You could use a VPN like okayFreedom and they wond be able to track you. You can also use proxify. BUT REMEMBER, do not put in login credentials when using a proxy

Depending on how savvy they are yes. They could have a program running on another computer that keeps track of all websites you go to. They can also have tracking built in to the router (depending on model and firmware).

Most likely they don't know enough to do that.

The answer is a very definite "maybe". It depends upon how your parents have configured the network. Properly configured they can not only see what you are doing but also block you.

Maybe you should behave and there will be no problem. Sounds to me like there is a trust issue here.

My partner and i suggest applying http://www.vpnmaster.org/ to unblock web-sites. I am using their services for more than 2 years with no complications.

Yes, they can,

But you can browser that website in Private tab,

Or Use TOR browser, no body can trace, what are you doing online?

Even your ISP,

Best Regards