Teacher Trevin gave an excellent answer. For more details, you could consult English Grammar in Use, 5th edition, by Murphy. Unit 83 (... a friend of my sister's, ... a friend of Tom's) and Unit 109 (... I like my job very much).

Colloquially we say this! And yes, it can also be used in plural form (i.e. “They are friends of Luca’s”). You can also use possessive pronouns—“friends of his” or “a friend of mine”. While it may not make much sense grammatically, it’s very common. For your second question, “very well” should be at the end—don’t split the verb from the object. “I don’t know Luca’s friends’ girlfriends very well.”

Correct sentences: He's a friend of Luca. They are friends of Luca, or they are Luca's friends. You can not say : friend of Luca's.

For the sentence, "I don't know very well Luca's friends' girlfriends", whom is it whom you do not know very well? The way the sentence is written it is all of the girlfriends of all of Luca's friends. So, if Luca has five friends and each of them has five girlfriends there might be twenty-five girlfriends whom you do not know very well. If you want to say that you only do not know the girlfriends of Luca, you need to move the apostrophe before the s: "friend's". It makes a big difference where you place the apostrophe. In spoken English this is a disaster because you cannot hear the difference. The whole sentence should be rewritten for clarity since it is not possible to hear its meaning. As for "he's a friend of Luca's", my vote is with Karen. It's just plain bad English. That's what "colloquial" means, really. It's a mistake made by so many people that it will not make trouble for you. Safety in numbers! The problem with speaking in colloquialisms is that they vary from place to place. In some places, people will think it sounds just fine but in other places it might make a bad impression.

Also: I don't know the girlfriends of Luca's friends. It just makes everything clearer. 🙂