Is money earned from Google AdSense considered unlawful, knowing that the user has 100% control over the displayed ads and does not allow prohibited ads to appear, and that the company's money is mixed?

If it is established that you have full control over the advertisements displayed on your site, and you exclude every advertisement that contains a Shariah violation, and your fee for publishing the advertisement is known, then there is no harm in what you earn. As for the mixing of Google's funds and the fact that some of them are from unlawful sources, scholars have differed regarding dealing with someone whose wealth is mixed. The majority opinion is that it is permissible to deal with them, albeit disliked, as long as the transaction is not directly with the unlawful portion of the wealth.