"Are you new?"
Translation:Es-tu nouvelle ?
"Tu est nouveau?" is an informal way to form a question using inflection (you make it sound like a question by the way you say it). Est-ce que tu est nouveau could be formal or informal, its a little more hesitant- I would say that est-ce que is a really "safe" way to pose a question, because it can be used in ALL contexts- very few things in French can do that!
Yes it is literally Isabel - and I still find it helpful to say it to myself like that - but that isn't how you would actually say it in English, as it sounds a little awkward. So I say it in my head - is it that you are new? and then write it how I would say that in English, which would be : Are you new?
It does quite often, yes; as someone said above, it's less formal than a non-inversion method, and not used in written French as often. Sometimes the verb requires a minor modification with inversion, but this isn't common. The example I was thinking of is "Comment est-ce que je peux vous aider?" would be "Comment puis-je vous aider?" using inversion.
We don't contract "tu" even when the next word starts with a vowel.
We contract two letter words that end in the "a", "e" and "ı" if they are followed by a word beginning with a vowel. But we don't contract words ending in "u". So we contract "ta" and "te", "la" and "le" and so on, but not "tu" or "du".