The USDA, generally on the very safe but a bit paranoid end of the spectrum, says:
After eggs are refrigerated, they need to stay that way. A cold egg left out at room temperature can sweat, facilitating the movement of bacteria into the egg and increasing the growth of bacteria. Refrigerated eggs should not be left out more than 2 hours.
(They also say some very sad things about Easter egg hunts.)
So if you're being strict, three days would be way too long. In reality, you'd probably be okay. The chances of getting salmonella are definitely higher, but are presumably still small (though I can't say exactly how small, of course). Personally, given the price of a dozen eggs, I'd probably play it safe.
Another answer mentions that in the UK eggs are stored at room temperature. That's true in quite a lot of places, but I'm guessing that they've avoided the large temperature swing issue mentioned by the FDA, so if your friend's eggs were refrigerated in the store, the situation's not quite the same as in the UK.
There are three major things that will effect the "natural" shelf life of the compote, in that they could extend it considerably past the normal shelf life of the ingredients individually:
How sweet is it? If it is sufficiently sugary, to the level of a jam or jelly, the sugar in the compote will act as a preservative.
This is because any bacteria or mold that try to colonize the product will be dessicated, as water exits their cells into the sugar medium via osmosis.
The problem here is that sugar is hydrophylic, and will easily attract water from the environment when the jar is opened, or when a wet spoon is put into it. If the surface becomes diluted with water, and thus the sugar is less concentrated, mold can get a foothold. So this kind of product is best stored in the refrigerator once opened.
How acid is it? Very, very acidic foods are less hospitable to most pathogens.
How salty is it? This one doesn't usually apply to compote recipes, but high enough salt levels also make foods inhospitable to most pathogens, again due to the dessication of their cells via osmotic pressure.
The specific recipe you linked to--at least the compote portion itself, excluding the vinegar syrup and the rest of the recipe--appears to have none of the characteristics that lead to a long shelf life. It should be held no longer than its most vulnerable ingredient, which would be the weak sugar syrup, so it is probably good for several days to a week in the refrigerator.
Now, in general, things named compotes tend to be far sweeter, and far more acidic than the recipe you have linked to.
In these cases, as ElindilTheTall points out, a very, very sweet recipe (jelly-like or jam-like sweetness) will last for many weeks in the refrigerator, and a couple of weeks at least at normal room temperature.
Finally, many compotes are amenable to home canning, if they are sufficiently acidic.
Canning has risks, especially for botulism, so you should only use recipes and methods from a very reputable source when doing canning, to ensure that the product is sufficiently acidic to be safe for the canning method used. Follow all of the techniques and prescriptions in the methods, as well, but I won't turn this into an essay on canning, which is not my area of expertise.
For those compotes that are properly canned, you should get an indefinite shelf life prior to opening, as long as the seal on the canning jar remains intact.
Best Answer
Dehydrating food is a common practice for trekking and backpacking. Dehydrating vastly reduces the water activity in foods, making them a less hospitable environment for bacterial activity. You'll want to use a reliable dehydrator with a variable temperature setting, as different ingredients require different temperatures and times to properly dehydrate. I think it would be better to dehydrate your ingredients individually, then combine them into meals. For example, Backpacker Magazine has a handy guide with some good suggestions. Dehydrated vegetables have a very long shelf life. From my internet research, it seems that many folks recommend consuming dehydrated meat within two weeks. I'm not sure you want to freeze your products. They might become moist when thawing, thus beginning the re-hydration process before you want. This could theoretically impact safety.