As long as you have an approved adsense account and the new websites comply with the Adsense TOS there's no problem at all (adsense wise). However, what good will that do to you? You'd have to optimize the sites basically for the same keywords and make them compete with eachother. You might get more traffic than you get with one website, however, it will also take a lot of hard work.
You can even have adsense on two or more identical sites, as long as they are not against the TOS. Duplicate content is punished by G's search engine, not adsense.
Of course you can. You can have 100 websites in the same niche, as long as each of them provides unique content.