Learn English – How to ask someone about his/her kinship

In the first part, I would say:

Glasses suit you.

though it would be more natural to say:

Glasses look good on you.

Glasses should be treated as a mass noun, since you are not pointing out a specific kind. So no article is used. And suit is better than fit, since fit has more to do with size.

In the second part, I would say:

I think you should go for the blue one. It suits you because your eyes are blue too. So they match.

or simpler:

I think you should go for the blue one. It suits you because they match your blue eyes.

I agree with Joe Dark's comment: Where is your family originally from?

Additionally, I'll say that a lot depends on the tone of the question. I'm curious about accents, and often ask a person if I can't place his/hers. But knowing that this can be a sensitive issue for some, I often couch the question in some tentativeness:

I hope you don't mind my asking, but I'm where's your accent from?

For what you want to ask, I'd go with something like what you propose:

I hope it's not rude to ask, but you seem to know a lot about Italy; is your family from there?

Asking in advance for pardon and giving a reason to be asking will help, particularly if you're showing a genuine interest.

But in general, I think you're on the right track simply by being aware that this can be a sensitive question.