I'll take a stab at them, but bear in mind that my answers will undoubtedly be informed by the culture I grew up in (the USA). As you know, the US practically owns the entertainment industry, and artists from all over flock to New York or Los Angeles in an effort to "make it." Americans are avid consumers of entertainment, and the market is therefore rather large. However, the high arts—under whose umbrella I would place contemporary composers—are, by comparison, much less valued by society. (The selection of classical music on streaming platforms such as Spotify, for example, is abysmal.) This may also be true of cultures the world over; all I can speak to is my own culture, though.
In essence, I believe that the arts are what connect humans to the divine. I haven't heard of any other animal species being so moved by beauty that they devote their lives to creating it, or weep uncontrollably when confronted by it. For whatever reason, this divine connection is vitally important to humans, and artists have persisted in every culture and every society throughout history. Composers, of course, aren't the only ones who offer this connection, but we are the only ones who bridge that gap through music. (Some could argue that popular music can be divinely beautiful, too, and I won't disagree.)
I'm not exactly sure what you mean by "social purpose." If by it you mean "what is contemporary classical music's role in society," then I would say it fulfills the same role as contemporary non-classical music: it's a creative outlet for members of the culture. Whether it resonates with society is another thing entirely, and I suppose some of that depends on exposure, acclaim by the "experts," etc.
To be frank, no. The vast majority of humans are traditionalists (in my experience), and the thought of new and different is quite unsettling—to the point of near radicalization if such traditions are threatened. But these very people are our intended audience! I think it's inherent in the being of every artist to leave his/her legacy, and we feel that in order to do so, we must create "originally." Yet we overestimate what originality looks like, and off we go creating radical artwork that is really neither original nor art. As C.S. Lewis put it, “Even in literature and art, no man who bothers about originality will ever be original: whereas if you simply try to tell the truth (without caring twopence how often it has been told before) you will, nine times out of ten, become original without ever having noticed it.”
In my own limited experience, I find this to be accurate. It's why so much avant-garde music sits ill with me. Very little of it seems to be created in an effort to capture the composer's truth, but rather as a statement of, "I am radical and original. Accept me on those grounds or not at all."
We should rather be about creating truthful music and not working ourselves into a frenzy trying to be original. This, I feel, is the music that resonates with society: the music that speaks to the veracity of human existence. It doesn't have to be new, but it does have to be true.
As an expression of members living within a society, it does, indeed, have a function. How far-reaching that function is depends on the skill and intent of its creator. If, as a composer, your goal is for your music to sound like someone else's; or if, on the other hand, your goal is to sound completely original, I think you'll find that your music's function will be limited solely to your own personal enjoyment. The function of contemporary classical music, in my opinion, is to uplift society, to connect humans back to their origin, the divine—whatever you want to call it—through the expression of the composer's own personal truths via music.
***
So those are my thoughts. To summarize, my argument is that modern (contemporary) classical music, like all other artforms, is a means of supplying humans with a connection to the beautiful, the divine, etc. Unfortunately, our societies don't assign monetary value to that, so scraping together a living as a composer in that sense is exceedingly hard to do. And, I suppose that's why the questions were posed in the first place. Valuable services are financially compensated; modern classical music isn't compensated; therefore, modern classical music must not be of value. That's a valid logical construct, but the first assumption is incorrect: valuable services aren't always compensated monetarily.
The creation of classical music, as an artform, is and will be valuable as long as society produces people to craft it. Composers of it will almost certainly have to find other ways to subsist, but this doesn't undermine its value.