I'm afraid questions written in Italian won't be beneficials for people whose Italian skills are not developed enough.
Should we allow to write question/answers in Italian, or should we rather enforce all questions to be written in English?
About this question, I think we should apply the golden rule that says that everyone is free to ask questions in one of those two languages (we restrict ourselves to English or Italian, of course).
This makes sense because those who are learning the language wouldn't be necessarily able to follow a post if it is written in the language itself; native speakers could talk about the language using it instead.
This method is widely used on the German language SE and I think it works pretty well (I am one of those who wouldn't be able to use it if everything were written in German and I couldn't use it if no English were allowed, but if I want to practise some German I try to write with it and to translate the answers, it's up to me).
Moreover (this is added from the comments below) I think we should answer in English to a question posed in English and in Italian to a question posed in Italian, for the same reasons mentioned above.
I don't think we should delete them outright.
Questions should be preferably in English for the time being, although I wouldn't go as far as forbid Italian at all. I realize that sometimes asking a question in Italian is going to be much easier, so we should allow that.
Answers should preferably be in the same language as the corresponding question or bilingual. This is under the assumption that the OP is fluent in the language in which they choose to ask a question but not necessarily the other.
In all cases I fee we should allow the community to edit posts as to add both languages.
Looking at this question and at German stackexchange, I'd say that if Italian is used non-Italian speakers would be excluded (and that would be a problem since people learning it are likely to visit the site), so English should be the primary language. Moreover, stackexchange operators would not be able to monitor the content easily.
On the other hand, Italian only speakers may encounter problem, but in general English is the '''lingua franca''' of the internet and is required to use it proficiently, we can assume that people asking questions so particular to not being solved with a quick Google search in Italian are educated enough to understand English.
I would say that depends from the question: If the question is much relevant for people learning Italian, for example questions about the correct Italian word to use when translating an English word (provided the OP says what he is trying to say), then the question should be written in English.
The first language spoken by the user who writes the question should not be relevant, as I (an Italian) I could have a question about how to explain something to a friend of mine, who is American.
Maybe providing a question in Italian and English could be a solution, but I am not sure what the Stack Exchange planes are about internationalisation of Stack Exchange sites.