>Q1: Why wouldn't this container also cause criticality? Surly the point of the container is to prevent radiation from "leaking out" so why wasn't it also causing nutrons to reflect back into the core.

Criticality is extremely sensitive to both the material and the geometry. Lead is a good shield (particularly for photons rather than neutrons), but it's not a very good moderator. And the geometry is not necessarily the same between shielding and a reflector.

>Q2 If a container is necessary to prevent exposure how were the scientists able to move the core from the container to the experiment's equipment, i.e. the hemupheres.

Things like that can be controlled remotely. Or in the case of a critical assembly, the dose rate might not be very high when the system is not near criticality. So each part can be held individually without shielding, and only when they're precisely assembled in a near-critical state does the dose rate become appreciable.

>Q3 Is the amount of exposure from the core, in the timeframe of preparing and performing the experiment acceptable? (Q3.1) If the core was sitting in a table in a room, could I walk into the room, and sit at the table without serious exposure? Logic tells me this must be the case because scientists and assistants were doing exactly that, and everyone seemed to know that it was safe to be in the room during the experiments.

Yes, if it's not near criticality.

>Q4 As the core reached criticality does the amount of radiation increase steadily , or does it remain at a safe (acceptable) level right up until the point of criticality where it spikes massively?

It all depends on the specifics of the setup in question and what's considered "acceptable". As the system approaches criticality from below, the dose rate will increase. More details here.

>Q5. (The last one. Thank you for your patience). If the complete closure of the two hemispheres cause criticality, due to the reflection of the nutrons, why do those same spheres not prevent the radiation from "getting out". It seems contradictory to have total reflection and radiation leakage.

It's not *total* reflection, it's just *enough* reflection that on average, each fission neutron induces at least one more fission reaction. There are still plenty of neutrons which don't induce fission, and/or escape the critical assembly entirely.

So the demon core would’ve been used in a third bomb if Japan had not surrendered after the first two.

Were the cores of the first two bombs also called “demon” cores?

And why “demon”? Wikipedia doesn’t say.

https://en.wikipedia.org/wiki/Demon_core

Q4. It's important to understand the difference between subcriticality, delayed criticality, prompt criticality.

In a subcritical configuration, each neutron produced by fission causes fewer than one additional neutrons by fission. In e.g. pure Pu-239, each fission from a thermal neutron produces about 2.8836 additional neutrons, so as long as each neutron has less than a 1/2.88 = 34.7% chance of hitting another nucleus and triggering a fission, it won't form a fully self-sustaining chain reaction. But each neutron can still form a temporarily sustained chain reaction. If each neutron has a 33% chance of triggering another nuclear reaction, then we can calculate that each neutron would directly produce an average of 0.95 additional neutrons, and those 0.95 neutrons would produce another 0.903 neutrons in the next generation, et cetera. This turns into a mathematical infinite series whose sum is 19.16, so for every actual neutron produced by a spontaneous fission, we would expect an additional 19.16 neutrons (on average) to be produced by the chain reaction.

That might seem like a lot, but it's not. In a supercritical configuration, each neutron produces more than one additional neutron in the next generation, and the density of neutrons flying around increases exponentially with time. The demon core was about 89 mm in diameter, and thermal neutrons have a speed of about 2.2 km/s, which means that neutrons will either react with another neutron or leave the core within about 40 microseconds. If each neutron produces 1.1 additional neutrons, this means that the number of neutrons in flux at a given time will follow an exponential curve that increases by 10% every ~40 µs, which means that it doubles every 292 µs, or increases by 10.7x every ms. If you have one neutron at t = 0 ms, you'll have 10.7 neutrons at t = 1 ms, 19 billion neutrons at t = 10 ms, 3.89 • 10^20 neutrons at t = 20 ms, and by t = 30 ms the entire core will be a ball of plasma millions of degrees in temperature. Once you go supercritical, the reaction rate will rapidly increase faster than nearly anything can react, and your only protection from a runaway reaction and an explosion is generally the thermal expansion of the core itself reducing the core's density and reactivity to the point where the reaction is no longer supercritical.

But there's a caveat to that criticality threshold: of those 2.8836 additional neutrons, about 0.0065 are *delayed neutrons*, whereas only 2.8771 are *prompt neutrons*. These delayed neutrons don't come from immediate fission of a Pu-239 atom, but instead come from the radioactive decay of a fission product. This delay could be a millisecond, an hour, or a month long, depending on the half-life of the fission product in question. If the configuration of the reactor is such that the delayed neutrons make the difference between the reactor being subcritical and supercritical, then we call that configuration *delayed criticality*, as opposed to the prompt criticality described in the above paragraph. Instead of the time constant of the exponential growth function being determined by the very short travel time of a neutron, the time constant becomes roughly equal to the half-life of the isotopes in question. This slows down the reactor's supercritical chain reaction growth rate into something typically on the order of minutes to hours, which can easily be managed by humans, machines, or mechanisms of intrinsic stability (e.g. thermal expansion of the core or moderator). Nuclear reactors operate in delayed criticality. Plutonium makes only about 1/3 as many delayed neutrons as U-235 does, so the transition from delayed critical to prompt critical is much shorter for Pu than for U-235. This may have contributed to the frequency of accidents with the Pu-based demon core.

So getting back to your question:

> As the core reached criticality does the amount of radiation increase steadily , or does it remain at a safe (acceptable) level right up until the point of criticality where it spikes massively

Both. As it approaches criticality, the amount of radiation increases steadily, but it still remains at a safe (low) level as long as it's still subcritical. But as soon as its reactivity goes prompt critical, even if by only a fraction of a percent, the radiation starts to get very big very quickly, usually only limited when the heat from the reaction causes the core to expand to the point where it's no longer critical.