What stays on your device
Two things are saved, and both stay in your browser: the theme you choose and what you enter in the limit tool. Those two choices never leave your device. Visits are counted separately, without cookies, though the statistics service does see your IP address and browser.
Every paid link on the home page carries the label Ad and goes to the same single online casino partner. Each one opens in a new tab. Your browser does not pass along the page you came from, so the partner cannot see which page sent you. The site receives a commission via those links, and whoever the partner is could change. You will find none on inner pages, including this one.