I'm not as familiar with citrus, but tomatoes and peppers can develop something called blossom-end rot. This is caused by the plant not receiving enough nutrients (specifically calcium), whether b/c the plant isn't getting enough water and thus can't get the nutrients out of the soil or b/c the soil is deficient.
Regarding whether it's safe to eat, a tomato w/ blossom end rot is still safe to eat, once you remove the affected area.
I hope this is helpful!
Do you have a picture of the orange in question? That would help greatly with diagnosis.
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
Spherical or spheroidal foods are indeed the most likely to be implicated in choking - grapes are well known. But you're unlikely to get sufficient statistics to answer fully. Most of the medical literature I've seen is at least as concerned with size, and of course that changes as you eat the sweet. You'd have to start unusually small for size to be much help.
Hard edges are much less of a concern. You'd struggle to get them sharp enough to do any actual damage, and the corners dissolve fastest, meaning they blunt almost immediately. This also means that the corners of something like a cube will go fairly fast, and you'll be left with a near-spherical blob.
You might be best off with something like a coin shape - a flattish disc or oval. This is a traditional shape for barley sugars, and I've also had hard fruit sweets that shape. While coins do show up in the choking statistics, they're very common items for children to investigate, including by taste and when not supervised.