>Is it possible to actually completely eliminate illegal guns and ammo in private ownership?
No>How many firearms are secretly owned in places with extreme gun control and penalties like China and Singapore?
Probably less than countries where it is easy and legal to own one>Today with metal detectors and sniffer dogs it seems almost impossible if they search your house.
Guns can be printed in high temperature filament as strong as aluminum that will not show up with a metal detector and/or embedded in a solid mass with the same density. Dogs to my knowledge sniff mainly gunpowder and explosives ingredients of these. I don't think they can smell the actual firearm itself but they may be able to be trained to smell lubricant used for the firearm. You can avoid all of these threats I think. The cops will strip down everything in pursuit of the contraband if they think it is there but you can avoid that to to varying degrees based on threat model. There is this old rule of thumb for hiding drug stashes about like 15 minutes of hiding for 1 hour of searching ro something. Anyways figure out how hard the cops will go to find such contraband and prepare your model accordingly.>>3100
This. Bury underground in some preservative in some remote location on a property you own or somewhere else no one will dig through incidentally. Don't be caught travelling through such an area. Ammunition and small items can be buried in small waterproof plastic containers etc. There is even a lot of designs online for easily accesible buried waterproof containers. The prepper community etc has tons of good tutorials online. Don't just scoff at good ideas. Learn.