Yes. It is a big leap from a seven-year old boy firing off a cheap firework in his parent's backyard to men taking a rocket nearly 250,000 miles to the Moon, landing on it and hopping around, and then flying back.
Agreed. In the same way that it's a big leap from a seven year old boy making a paper plane to an A380 flying hundreds of people around the world with every seat having an entertainment system with a wide selection of movies, TV, games and music. Comfortable seats and bathrooms, hot food. On board Wi-fi. Flat beds and showers in business class.
That is a big leap, but like most advances in technology it was made as a series of "small steps for man", not one "giant leap for mankind".
But an ICBM isn't designed for space travel -- it's a military weapon. And going from, say, 5,000 miles of range to 250,000 miles (plus a return journey), seems a massive leap.
Again, correct. But same argument as above, the leap was made as a series of small steps. It was the Saturn V with several stages of rockets which was required. The Russians were working on similar things, the US just got there first, the Russian ones kept blowing up. One thing to note, once you've escaped earth's gravity and made the initial burn to set you on course to the moon you don't need any more fuel to keep going. You're in a vacuum, there's no drag. Earth's gravity does slow you down but you don't need to keep your foot down all the time because of how fast you're going. It might be 50 times further but you don't need 50 times as much fuel, most of the fuel is used in the initial escape from earth's gravity.
I'm still unconvinced, too, that there is much to gain from sending people into space. Doing so was demonstrating political power and supposed scientific prowess originally.
The space race was initially motivated by political one-upmanship. But because of that they'd have surely been very keen to call the other side out of they could show the other side was faking it. It's notable that neither side did. What is to gain from ongoing things like the ISS? What is to gain from a permanent base at the South Pole? Or from people keep climbing Everest. As a species there's something in us which wants to explore, wants to learn more.
Yes, NASA did do things which no-one had done before. But before that the Russians did - Gagarin was a massive milestone. The Wright brothers did things no-one had done before.
By definition, invention of new technologies requires doing things no-one has done before. But Kennedy threw a shit-ton of money at the problem to overtake the Russians and as we see in War times, technology can progress quickly with the right motivation. Apollo XI was the culmination of years of work. Note the XI, there were 10 previous missions during which many of the techniques necessary to get to the moon and back - docking, EVAs etc - were practised and rehearsed. And prior to that there were the Mercury and Gemini programmes, much was learned from them.
I'd highly recommend "A Man On The Moon" by Andrew Chaikin if you want to learn more. It has loads of detail about how all this was done.
There were a load of small steps leading up to Armstrong's small step which represented a giant leap for us as a species.