How do I take color Input from users and change color of WIX elements accordingly?

Depends on how your color is setted up in your DATABASE (or in your case → in the INPUT).

$w.onReady(function () {
    const bigBox = $w('#box0');
    const firstCircle = $w('#box1');
    const secondCircle = $w('#box2');
    const thirdCircle = $w('#box3');
    const fourthCircle = $w('#box4');
    const fifthCircle = $w('#box5');
 
    const changeBoxBtn = $w('#changeBox');
    const colorInput = $w('#input2') ;

    changeBoxBtn.onClick(event => {
        bigBox.style.backgroundColor = colorInput;
        bigBox.style.borderColor = colorInput;
    });
});