The frog thing is a myth. The frog will jump out when he gets too hot. Also, throwing a frog in boiling water will kill it instantly.

It's not so much an impenetrable barrier but it just gets way too hot down that far. The rock starts acting more like a liquid at higher temperatures and fills in the hole. The drill breaks down faster too.

No, that's not quite right. Water vapor is definitely a gas, you can't see humidity. Clouds are a suspension of liquid water in the air, not water vapor.

So the idea of half-life is a bit simplified for biological processes. The way half-life is taught in school is usually with radioactive decay. Radioactive decay follows a first order rate of reaction. What this means is the rate of reaction is directly proportionally to the amount of substance. If you have half as much, it decays half as slowly.

Many other reactions have more complicated kinetic orders. There are second order reactions where reactions go four times faster if you double the reagent. Zero order reactions where the rate is not affected by the amount of something. You can have fractional order reactions that speed up as the concentration of a reagent decreases. A reaction can also have different orders for each reagent or even be catalyzed by some small amount of something to speed it up. Also, there can be a limited amount of certain reagents in the body meaning the order of the reaction can change as something is broken down.

So, for instance say you have a drug that is a zero order reagent. It is broken down at a rate of 1 g/hrs. You take two grams. Half life is 1 hour. After that hour, half life will be 30 minutes. 30 minutes from that, 15 minutes. You get the idea.

Finally to answer your question, the half-lives are written at expected does. It can not necessarily be extrapolated to tell when it will all be out of the body, but it is a useful tool for healthcare providers.

An identical twins organs should not be rejected but then then twin would be without their organs. With a leg the nerves and blood vessels won't have grown the same way so it would still be an incredibly complex procedure.

There is still a lot of research to be done with stem cell organs. Not sure why the other guy said it was prohibited. It's one of those things that is always a few years away so who knows.

Prosthetics. The lower limbs are simple enough that you can use a fake one and still get around for the most part. They've even got those special legs for running that are banned in the Olympics for being too fast. It's just not worth the risks from transplants. With transplants, you have to take immunosuppressive drugs for the rest of life and your body will still eventually reject the donated organs.