Say a group of silicon-based aliens arrive on earth, would their bodies be able to extract any nutrients from carbon-based food?
Silicon bodies, carbon energetics.
from my answer here:
Your opal creature uses silicon for its body, but has conventional carbon energetics.
When we eat, we use our food for two things. We metabolize some for energy and we use some for anabolic processes - building our bodies
There are creatures who split these functions. Iron oxidizing bacteria, for example, have bodies made of the same sorts of carbon molecules that we use. But for energy, they oxidize iron. They do not use the products of their energy metabolism for any anabolic process - the iron oxides are waste.
Your creatures use silicon to form their bodies. They are opalescent creatures, their bodies laid down from layers of soluble silica. Energetics however are much like ours - they oxidize oxidizable carbon and retrieve the energy.
It is not so outre. Consider our own bodies. They contain a huge amount of calcium, as bones. Can we "calcium creatures" eat glucose? Sure! We cannot use calcium containing molecules for energy. We must obtain the calcium in our diets and then process it into bones, which costs energy to do but makes us awesomely bony.
So too your creatures. Their bodies are made in large part of silicon and silicates or siloxanes. Their energetic biochemistry is similar to Earth life, either reducing or oxidizing carbon containing molecules to release energy. That energy is then used to do silicon chemistry just as we use energy to do calcium chemistry.
In general, as L.Dutch wrote, a silicon based lifeform will typically be unable to process carbon-based foods.
But since this is Worldbuilding, and you might need a different answer for your story purposes, let's look into ways to make it possible.
A hint in advance: I'm not a biologist. So I may be horribly wrong in what follows.
Our bodies, and those of any larger creature, are home to myriads of microbes, of which be benefit, as they do from us.
To the best of my knowledge, there are microbes on earth that are able to break down rocks. On top of that, it seems that there is no (chemical) task you could think of without somebody somewhere finding microbes that already do that job. I'm probably exaggerating, but the general principle should hold.
So, your aliens are space-faring. That means they are technologically advanced, and by a lot, compared to us. They will surely know in advance what type of planets they will be visiting. It's unlikely they just stumble upon earth, Columbus-style or such. That means they will come prepared to facilitate their survival in the environments they encounter. Being technologically advanced, they may very well have bio-engineered some of their gut microbes so that those digest our carbon-based food and create silicon-based food as an end-product of their digestion, thus enabling your silicon-based aliens to benefit from carbon-based food.
Most likely not, in the same way no life form on Earth can extract nutrients from eating silicon based compounds. The closest thing I can call out of my mind is chicken eating stones to help them break food in their stomach and to get elements for the egg shell. But that's not made of silicon.
Moreover, a silicon based life form would be adapted to process silicon based compounds, with silicon adapted enzymes or equivalents. Enzymes are so specific that we are not able to digest cellulose, though it's made from chains of glucose. Imagine how big is the jump between carbon based and silicon based molecules.
Depends on what you mean by 'eat', and what you mean by 'life forms'. Silicon-based life could mean robots or otherwise mechanical creatures, they could take in the carbon-based items and burn it for fuel/energy. It's probably not going to be an efficient form of energy extraction unless they're built to harvest the joules that way, but it's certainly an option.
As for whether or not an actual living thing based in silicon instead of carbon eating carbon-based things, that's probably not going to work out. I don't think I've ever heard of something eating sand and getting nutrients from the sand itself. Maybe the tiny life forms in the sand but not the sand itself. I'm now envisioning a beach of carbon, the dark sand contrasting with whatever you have for oceans against the sunset, with a silicon crab seemingly eating the carbon sand only to spit it back out once it's done filtering what can sustain it out of the grains.
This is implausible, since it's enzymatically unfavorable for a silicon organism to evolve enzymes to break down carbon organisms. After all, all the organic parts are immediately unusable for materials. But with a little manipulation, there could be benefits. There would also be large numbers of compounds in organics that would be poison to silicates, and the biological solvents would need to at least partly match up.
- Plants are able to trap and decay animals to extract minerals like nitrogen from the animals, despite the plants not classically "eating" the animals. this is because the animal contains something useful to the plant. So if the silicon organism wants soluble iron, or sodium, or something like that, they COULD get it this way. It would be pretty inefficient, but not impossible.
- I do agree (+1 Burki) that a hybrid organism (like a bacteria that is designed or evolved to use both carbon and silicon) could likely extract chemical energy and possibly some limited compounds (like ammonia) from the carbon-based food, then produce food usable by the silicon organisms. Again, this is likely to be pretty inefficient, but a species of great intelligence and limited imagination (or some other compelling reason like a genetic obsession to hunt and eat prey) could obtain at least partial nutrition from carbon-based food.
The silicon based organisms cannot survive by eating organics but organics carry trace elements that might be energy intensive to sift out of raw rock. Thus, they often eat organics to gain a low cost source of those trace elements.
Humans (and some other animals in Earth) often eat poisonous compounds to get high. Organics may be poisonous to silicon based life forms. However, in the right doses, they can cause various effects (getting a buzz, getting hammered, hallucinations) that they might enjoy. "Gerbils make me jittery but oak is groovy..."
The former would probably be a good material for teeth (or skin scales or anything like that) and the latter could be used as analogues of blood, fatty tissue and for covering the bending parts of the limbs of your creatures.
So it could even be essential for silicon based creatures to ingest (at least some amount of) carbon or even carbohydrates.
Yes, given appropriate "circumstances", it could be the case.
This subject has been "entertained" in research and, in fact, relatively recently. The link points to an article (official scholarly reference here), which describes how scientists managed to slightly manipulate an enzyme from an extremophile bacterium and inject it into E. coli, which, given the "right" precursors, can catalyse the formation of carbon-silicon bonds. This is akin to carbon fixation (formation of organic carbon compounds from inorganic carbon).
Now, look at that! You get both elements at once, in living cells. These can be cultured in appropriate silicon-containing growth media and used as food by your aliens. If we are going to assume your aliens are like the "humans of their own environments", it is much more likely that they will have enzymes to break down such "organosilicon" compounds and suitably utilise that silicon, than to have the appropriate machinery for "silicon fixation" from "raw" inorganic silicon.