> When I use google to search for this website, under the link for the home page - there's a text that's not actually on the web page (looks like ads)
Most likely stale cache from previous owner of your domain, of which there has been plenty[1] or was parked in-between.
Setup google webmaster tools for your domain.
>It's a one-page site in Html, how can static Html be hacked by hackers?
Plenty of ways, the source in your computer to the server which hosts your website. Using static website just limits the attack surface from the website itself.