I've seen some sites that make items that are translated with Google Translator and then put on the blog, because the articles are not very well understood. Can we do this using Adsense? That is, I can go to the Google page translator, translating an article on my blog and paste it as a new post in my blog?
You dont need to do that. Just place the google translator links on your pages and the translator will show you the translated pages, if your worry is about adsense income, then dont worry the ad codes shown on the translated pages are yours only. If you are planning to put translated pages on your own blog server, then be careful since the language needs to be supported by adsense as you might remember that you have put in a primary language when you signed up with adsense
But, I can write in other language...or not? When I signed up with Adsense is for my primary language or they restricted 1 language?
You can write in other languages. But don't use some automatic translators, it's going to be garbage, hire people for that. you cannot put Adsense ads on a page filled with gibberish.