The animal you're asking for is known as Homo sapiens.
Sorry, but you're essential describing many actions which pretty much involve human-levels of intelligence,and the animals which have similar intellect will not be hard to notice (unless you're blind, though you'll still hear the death dolphin squirming towards you to do to you what it does to fish, or if you live in a place where it's common to find chimpanzees or crows inside of buildings).
But given that you're also including prehistoric creatures (which is NOT the way to go if you want intelligence. The mighty raptors Hollywood showed us could apparently be outsmarted by your average dog) and admitting both the classic meaning of animal as well as some impossible bioengineering in here (since you're willing to use breeding to achieve the traits you desire, plus you don't seem to mind bringing back extinct creatures, which could only happen through either this or a time machine), my bets on a non-human assassin animal would be on a genetically modified Giant Pacific Octopus.
Octopuses in general are in many ways nature's coolest assassins. They can't fly silently like an owl or slash you with claws like a lion. But it is known to be a very intelligent animal, can change both it's color and texture despite being colorblind, are stronger than a human and, one of the best: they can essentially fit inside any place larger than its beak, which is the only hard part of its body (so essentially any place larger than a penny will do). The giant pacific octopus, while also having many of these qualities, is larger and stronger than a human, and is known, like its fellow brethren, for being troublesome in aquariums due to their attempts (at times successful) of escaping their enclosures.
So let's see if this bioengineered Giant pacific octopus could fit the mold according to what a giant pacific octopus can already do without modifications:
The animal must be smart enough to understand which person to kill and which not to
Octopuses are capable of recognizing and remembering by sight and taste, so this is likely already doable with a normal octopus.
be smart enough to find their victims.
How does it work? The government leaves an object hidden somewhere near the house of the victim, the object emits a smell or sound only the creature can hear from really far distances. The further the better.
Otopuses have been shown to be able to transverse mazes, solve puzzles, and open jars with crabs inside by recognizing the food. Though I doubt smell or sounds can work, but if you have a layout of where the victim will be, making them go through a similar maze will let him learn where to go and how to come back. Also putting special fluids in the path it must go might also work, as it can taste its surroundings with its sucker pads.
The animal must be trained to understand kill commands through simple communication.
If it can work with vocal orders, even better.
Relying on voice won't work. They can feel variations in pressure with their skin, but that is for when they're underwater. Rather than colors (they're colorblind), showing special shapes might work decently well (show a crab sign and it could understand everyone must die) this one might require a bit more of bioengineering and conditioning to be properly tuned.
the animal needs to be smart enough to find signals from really far away and track down the house, be smart enough to understand basic communication and most important of all, be really fast at killing and really good at escaping.
Finding signs? No issue. Understand basic communication? I wouldn't say communication (especially not vocal), but it can understand signs and remember situations. Kill someone fast? Depends a bit, but since they can overpower sharks and humans alike, I see no reason why it couldn't learn how to quickly twist or break a neck, so not too crazy. Really good at escaping? Absolutely. Not only it can squirm inside places its potential pursuers could only dream to be able to access, it's ability to change color and texture can make it a challenge to see them in the first place (also many octopuses have poisonous saliva, with the blue ringed octopus being one of the most venomous animals in in the world, so with some bioengineering we can give it that weapon too).
run away after a successful kill, even if injured, that's better.
Many octopuses can heal entire arms in case they're lost (and at times will rip it off themselves in mating season), so clearly doable so long as there are enough arms left.
An animal which can ignore pain and still run is preferred
They can loose arms and escape and they can feel pain, it already happens in nature.
The animal should try to escape without being followed, if people are following it, it should be smart enough to not return to it's master until it is safe to do so.
This might be assured with some bioengineering, but given octopuses already have prey behavior and will camouflage and stay on low profile when chased by predators, it's clearly not a stretch (though I'd say den rather than master, as octopuses aren't quite social, but given that octopuses seem to have spatial memory it can likely avoid it's meeting point until it's safe).
If possible, everyone should believe the animal is a demon sent from hell to punish sinners and when it disappears they will just think it went back to Satan.
Well they look more like cthulhu than Satan. But since Chapodiphobia (fear of octopuses) already exists, I'm pretty sure such an assassin can easily leave people (and especially Japanese schoolgirls) terrified.
To summing it up, we have an animal that, at least in a way, can already do a variation of most of what you need it to, is considered to be extremely intelligent (one of the most intelligent invertebrates, which is still impressive despite what it's competing against), already capable of briefly leaving the water (some species are adapted to crawl around on land for short periods), can climb walls in some cases, if the surface is smooth enough to allow for the use of their suction pads (they're not capable of doing it indefinitely, but they're still strong enough to carry their 182 kg bodies vertically), have apparently preemptively killed sharks under fear of being attacked, are incredibly curious and are capable of learning by watching others (which is more of a big deal than it might sound).
So, with some adaptations to allow these animals to breathe and survive on land (maybe through a buffed up version of lungfish so that they don't completely loose their water breathing capabilities) and a boosting of their circulatory system to allow for a more active creature, as well as some boosting of their intellect and some modifications to the beak so that it's closer to a Humboldt squid's and maybe boost up its poisonous saliva to be as lethal as its blue ringed cousin's, we could essentially have a creature that, despite clearly sticking out like a sore thumb and not being the fastest one, is capable of adapting to situations, has incredible camouflage (let's hope the targets aren't fans of smooth surfaces though), can overpower a human, can fit into very small crevices and essentially disappear, could potentially recognize a target and look for the best strategy to attack and can remember about their surroundings, facilitating its escape.
Note:while I know octopuses aren't the smartest ones around and are clearly not adapted to living on land, I do believe they're one of the best fits for the "silent but deadly, hard to contain, cunning assassin" stereotype after us. The ideal scenario here would be to simply grant it a human's intelligence to maximize its effectiveness.