Yes - we do think the app can help you with bad habits you've picked up in English.
That said, it's important to know ahead of time what the path ahead of you looks like, so that you don't get discouraged. Once you have ingrained bad habits, you don't really get *rid* of them; you build new, good habits *next* to them and start using those new habits often enough that they become more and more comfortable for you to use.
So with pronunciation, you will have the ability to speak English with an Italian accent. As you use the app, your ears will get better at recognizing what a good accent sounds like, and you should find it easier to make an American accent. At first, that American accent may feel a little fake or silly, like you're pretending to be some American actor. But the more you use it, the more natural it will become, until you use it more often than your Italian accent.
On the grammar/vocab front, if you have a habit of translating, that should naturally fall away in time, as you do a lot of exercises where you're memorizing English words *in English*. Those kind of immersive tests will push you in the direction of thinking in your target language. One hint, in terms of strategy: don't spend a lot of time making flashcards for words and parts of grammar that you know already, even if you only know them in translation. Instead, focus on new words and new bits of grammar. You'll progress faster, and the old words will show up in those sentences anyways.
Best of luck!