Well... the rate of decay is a measured thing after the atoms decay... its statistics, not science. For example: if you throw a coin, as we usually dont know anything about the movement of it, statistics will say that, in average, the chance of you get heads or tails is the same. So, if you throw several times, you would get about the same number of heads and tails. But the coin doesnt know that it must respect an average. If you throw the coin and get heads several times repeatedly, the chance of getting a tail wont be any greater because of this. What the coin does is governed mostly by chance, and statistics is only an way to disguise our lack of better knowledge about the matter being studied.
So, as we know that the coin has two sides, we assume that the coin will fall with one of this sides upside. But as we absolutely dont know what the coin will do, and thus would be prejudiced to say that one side has greater chance of being upside, we say that the chances are the same for the both sides. But its only a nice way to say that we dont know anything about it. (Statisticists forgive me, but its true... )

Regarding the specific example of radioactive emission... the atoms nucleus can be viewed as a cloud of flies flying around a lamp. The flies being the protons and neutrons, and the lamp being nothing. (The protons and neutrons are attracted by themselves, but the flies are not... thats why they need a lamp). Anyway, details aside, the fact is that the subatomic particles are in movement into the nucleus. When two particles fast enough collide, they emit radiation.
But we cant know (due the uncertainity principle) the position of this subatomic particles, so we cant know when they will collide and emit radiation. And nor they (the particles) do, they dont know that the kind of atom they are part has some measured decay rate. The particles just spin around, carelessly, until two of them collide. And as nor we nor they know when they will collide, we say that it happens by chance.

There is a chance of get 10 tails repeatedly when throwing a coin. There is also a chance to get, lets say, 100, or even 1000 tails repeatedly. But we dont see it happening because its very improbable. (about 1:1,000,000,000 for only 30 repetitions). We could make a law like "one coin never falls with the same side upside for more than 30 consecutive throws", and this law would only be wrong at about 1/1,000,000,000th of the time. Increasing the number of maximum throws, the range of validity of this "law" would be greatly increased. But it wouldnt be a true nature law. Cause there is nothing that forbide a coin to fall heads or tails repeatedly by any number of times. If one were lucky enough it could be done. So, again, statistics shouldnt be used as tool for making laws.
Of course sooner or later the atoms will decay... but its by the same reason of why we cant get more than 20 or 30 (or even 10) repeated heads or tails throwing a coin. By chance (or lack of luck).
And yes, even the most improbable things are allowed by physics to happen, but as the chance of they happen is VERY small, we say that its impossible for all useful purposes.

I dont know... i think that what we call rules or laws are patterns noticed by our minds... but nothing ensures us that the nature must obey the patterns our mind makes...

Me too... and as understand what you say about realizing its limitations, cause i feel it myself too... thats why i started to search other things.
And the numbers only remains constant because they are defined as constants... if they are, by definition, constant, they just cant have any hope of changing their status. For them the life is deterministic indeed...

Man... its a very broad question indeed... i wouldnt know even for where to begin... if you could make it a bit more specific, i could try to answer.
And please dont think about starting some "coelhoism"... i think the world is already full enough of "isms"...

Man... it happened the same with me when this thought appeared into my mind at the first time... i was high (as always ) and noticed that this picture was a very good analogy of the relationship between observer and object...

It wouldnt be incorret, but incomplete. The filtering done would erase some information, and so we always would lose some knowledge.

Yes, it does. But then we should admit that our knowledge and even our "theory of everything" would not be actually a theory of everything, but only a theory of what we can understand and percieve, and be aware of its limitations.
So, for example, physics would be called "Mathematical patterns of the universe when observed by the human mind", and not "The Laws of Nature".

Well... i dont want go off topic so i wont enter in details... but i believe that what we call reality depends heavily on how "tuned" (actually like a radio) our mind is with the reality. Like, when we are stoned our mind is "tuned" differently than when were sober, we percieve things differently. So, our notion of reality depends on the tuning of our mind. If we tune it in some very different "station", the reality we will percieve will be very different from the usual, and surely will have its own laws that may be different of the ones we notice when sober.
And if it actually were so, as there are several different "tunings" of the mind, there would be several sets of laws, one for each tuning.

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"Everything we do, everything we are, rests on our personal power. If we have enough of it, one word uttered to us might be sufficient to change the course of our lives. But if we don't have enough personal power, the most magnificent piece of wisdom can be revealed to us and that revelation won't make a damn bit of difference." Don Juan Matus - Tales of Power