PLEASE HELP! Is my mac hacked?

My mom thinks my macbook pro has been hacked and she's freaking out, though PC security software shows there's no problem. I have few knowledge about this. PLEASE help me figure out if my mac is hacked/if there is any problem.

I've used Wifi modem at home until a week ago, and something weird happens. Whenever my mom changes the name of wifi we uses, the wifi disappears from the wifi list and re-appears in the list after a couple of minutes with the original name, but without the lock icon (so it's open to anyone without password). She tried so many times but failed to change the name. So she thought the wifi network account was hacked and turned off the wifi modem. She used another modem to connect my macbook to ethernet network and everything worked fine.

Just two days ago, when I started the macbook, it could not be connceted to ethernet. So I opened the system preference and clicked 'Network', there were several options like 'I use Airport to connect to wireless network', 'I use a cable modern', 'I use a DSL moderm' and 'I use a local area network (LAN)'. It was setted to 'Airport' option though my macbook was connected to ethernet cable. My mom thought this is so weird and somebody has setted the option on purpose, so we cannot connect to the ehternet network. A few hours later, it was finally connected to the ethernet but it showed two locations. (Under the location bar, my mac shows 'home' and 'location', 'home' has five network on the left side list and 'location' shows none)

My mom called Apple store and restored the macbook to the factory settings. She didn't sign in with my original apple account or make a new one. When she started the macbook, Keyboard Setup Assistant popped up.

After pressing the key 'z', the spinning wheel appears and it took more than 10 minutes for identifying the keyboard. And ethernet was not connected again. So my mom thought somebody hacked the cable modem and installed some hacking tool pretending to be the Keyboard Setup Assistant.

Now she's freaking out and tells me not to use macbook at all.

Please help me figure out if there is any problem with my mac. (I also want to know why it is setted to 'Airport wireless network' option though my mac is connected to ethernet cable.)

PLEASE HELP!!