Could We Fly Or Survive Nuclear Blasts With Genetic Mutation/genetic Engineering

Are cockroaches the only creatures that will survive a nuclear war?

Nope. Quite a few insects are radiation resistant, and many are even more resistant than roaches, such as fruit flies and wood boring beetles. Smaller organisms will fare even better. Water bears (Tardigrades) can resist the vacuum of space, and will probably survive nuclear fallout well. The most nuclear radiation-resistant organisms are certain bacteria, such as Deinococcus radiodurans. As its name suggests, it can survive extreme radiation. Some bacteria even live inside nuclear power plants.Cockroaches and radiationNature has a way of recovering. Radiation dissipates eventually, for example, and animals adapt. Take Chernobyl, for example. Despite experiencing the equivalent of a small-scale nuclear apocalypse, nature is retaking it, and it's even safe for humans to visit... for very short periods of time.Chernobyl travel guide - Wikitravel

Can a human being, due to an extremely rare mutation, have an IQ of over 1000?

At this point, our current intelligence quotient scale definitionally doesn't allow for an IQ of 1000 (or anything close to it, for that matter). Less than 0.1% of the population scores below a 60, and the same is true for people with an IQ above 140. As IQ relies on a bell shaped curve (with ~100 as being considered "average", and over 2/3 falling between 85 and 115), it is impossible for any test or metric in existence to meaningfully test above a 200.That being said, an individual with an exorbitant IQ score (as you have suggested) probably wouldn't even be considered human at this point. If something like this did happen, most biologists would be compelled to accept that, effectively, this could be classified as a speciation event. If we were to draw a comparison, the difference in intelligence between this superhuman and those considered "geniuses" today would be several orders of magnitude greater than the difference in intelligence between our general population and rats, for example. Even if this did occur, the level of intelligence would be so out of the scope of our own human perception that we wouldn't even be able to comprehend the difference from "greatest minds in history". To take the analogy one step further, would a rat be able to even begin to perceive mathematical concepts, let alone something like quantum mechanics? So perhaps, maybe an individual you described would indeed "put to shame the greatest minds in history", but only from an omniscient perspective. This immense difference is something we couldn't even hope to understand.From a biological perspective, and considering limitations in gentic mutations, such a drastic leap would be absolutely impossible in one generation (i.e., for such an individual to just be simply "born"). Changes in cognitive structure caused by DNA mutations would occur on a [relatively] small scale. However, hypothetically, even the results of artificially selecting/breeding genius-level individuals over generations would take at least thousands of years to be distinctly observed. Unfortunately (or fortunately?), the limits of Darwinian evolution and natural selection prevent something like this from ever happening.