Can I put resin aquarium ornaments in boiling water for sterilization?

Aquariums should replicate as much as possible the natural environment. Plastic is not natural. Cement is not natural. You are better of using stones and hard wood. You can build anything you want with these.

What is even better, is that you can even boil them as much as you want, without significant negative side effects. I mean, boil the stones and the hardwood before cooling them and adding them to the aquarium, not boil the fish :)

I think your English is good enough, I'm not native as well but I can understand clearly your whole question despite some imperfections.

I've seen an advice on sterilizing these aquarium decorations saying that it's okay to boil them in water, but personally I wouldn't recommend it nor do it myself with decorations made of synthetic resins or polymers.

Also, by the way, an issue like this is one of the reasons why I would completely recommend against using second-hand ornaments at all. It's wise that you want to sterilize them, because one doesn't really know what was the fate of the fish that inhabited the previous aquarium with these ornaments and whether maybe a disease outbreak caused all of them to die - but sterilizing them safely and reliably raises a whole new plethora of problems. But I am going to answer further, in case you were going to use them anyway in your aquarium.

Firstly, your concers of the decorations potentially leaching harmful compounds during boiling are absolutely justified, because as far as I know most types of synthetic polymers and resins release chemicals if exposed to boiling water temperatures. I don't exactly know what type of material your ornaments are made of and thus I can't state with full conviction that it would certainly harm your fish or poison your cookware - but I will say that it's certainly a risky game to play to put any synthetic resin or polymer in boiling water if it wasn't explicitly stated to be both food-grade and designed to be used in boiling water temperatures. And for this reason I think these ornaments should not be considered safe to sterilize with this method.

What is more, even if these released chemicals were to be harmless or not released at all, you risk severely deforming and destroying your ornaments because in 100 °C some polymers will soften enough to flow, which would disfigure the ornaments into a miserable, melted mess.

As for cleaning I would suggest using a saturated water solution of table salt, it doesn't matter whether it is iodized or not. But table salt sometimes contains anticaking agents and it's recommended that one should avoid using such salt in aquarium settings. It could be problematic if it was to be used as a salinity source in marine aquariums, but actually shouldn't be an issue if we consider using it just for cleaning purposes - anyway, I'm including a note about this. For this reason, a special type of aquarium salt exists and should be readily obtainable in your local pet shop.

Salt is not as powerful disinfecting agent as for example bleach or isopropyl alcohol, but the latter two should not be used in aquarium cleaning because you risk fatal poisoning of your fish. I can't really guarantee that it will be fine though: salt would probably do it's job, but the best I could recommend would be using brand-new ornaments.