I've tried to Google the answer but I can't seem to use the right wording to get the answer.
I live in a building where there is free (Wired) internet offered in every apartment. Of course, I understand that by connecting the wire to my laptop, whoever administers the interenet (LAN ??) in the building, could see my internet history.
If I were to add my own Wifi router and secured it by password using WPA2-PSK, I understand that I will somewhat secure my WIFI broadcast.
But will this option offer any added protection against my building internet (LAN ?? ) administrator from searching my internet history: such as (internet banking / websites to download large files / ...etc)
Yes, using your own router adds the protection of having your own network protected by the router's firewall. It's no different than using a router to connect to your cable/dsl ISP. In either case, you gain the same protections. You are, in fact, treating the apartment's internet connection as your ISP!
That said, just like your cable/dsl ISP, it’s still possible for someone to eavesdrop on your activity as you traverse the apartment's network. And therefore, just like your cable/dsl ISP, you might want/need to consider a VPN to protect your privacy. Just depends on how much you consider this a threat.
We had a similar question recently in a University lodgings situation and the wireless router had been identified by the system and connection barred. Your building may have the same protection against a network within the network.