Your digital o-scope is aliasing the high frequency content of the modulated waveform. This is a common "feature" in digital oscillosopes.
You have the time base set to show the modulating signal (orange trace) and no problem here so far but the o-scope won't be sampling at its full bandwidth because it doesn't need to. If you turned the timebase up to run more quickly you'll get to a point when you start to see the carrier frequency in all its glory.
Here is a decent document that shows what happens and here's a little video you can watch.
Your understanding of what the IDFT does is simply wrong!
you don't get
symbol1 symbol2 symbol3 … symbolN
one after another in time domain, you get all these symbols modulating the complex sinusoid, added up.
If it is, then the OFDM should not have the higher transmission rate or speed, because it costs the transmission time the same with the original modulation method that without the OFDM modulation.
That however is still true: OFDM doesn't "cheat" physics. You take a channel of bandwidth \$B\$, divide it into \$N\$ channels of bandwidth \$\Delta f = \frac BN\$, and then you send \$N\$ data symbols at once. So, that's basically \$B\$ as a symbol rate (not accounting for sidelobes and empty carriers).
In a simple single carrier system with the same pulse shape (sinc), you'd get \$1\$ symbol with a rate of \$B\$. The same rate.
So, OFDM doesn't increase the amount of data you can send over one channel inherently.
What it does, however, is split the channel into subchannels, which then are easier to equalize. That's the main thing there is to multicarrier systems like OFDM: You reduce the (very hard!) problem of a wide, frequency-selective channel to \$N\$ easier problems of flat subcarriers. OFDM systems always pick their \$N\$ accordingly to make sure fading is flat within one subcarrier.
Best Answer
In a nutshell: One antenna will give you a usable radius of 100...1000 km, depending on the power used.
In Germany, for the example of my favored news station Deutschlandfunk, we used to have two long-wave AM stations (153 and 207 kHz, IIRC), and I do miss them every once in a while. The one at 207 kHz covered pretty much all of Southern Germany, and while I admit that the quality was low (as in: landline telephone-ish low), you could listen to the program with no trouble, anywhere in your house, and understand every word well.
Now, for terrestrial distribution, they just use FM, which works in a few small places only, or you could try DAB+, and I'm not sure if the latter works in all places. I do miss the robustness and the beautiful simplicity of long or medium wave AM.
It's not so much the type of modulation (AM vs. FM). It's the low-ish frequencies that tend to work well over wide areas and even through big walls, for example if you're downstairs.
It's not true that no one ever listened, and in contrast to North America, for example, Germany used to have only very few good stations on AM in the decade before they pulled the plug on it, which gives you another very important reason why few people listened.
A personal note: It twists my stomach to see how AM has already vanished, and to know that some want to abandon analog FM as well.
If you were to get cynical, you could argue there is some strong political will to seriously srew up anything terrestrial for good, at least in Germany. A bit off-topic here, and a rant, but terrestrial TV broadcasting shows you how bad it can become, and it's a fine example of unclever engineering: Analog terrestrial TV was shut down not long ago, in the early 2000s, with DVB-T as a replacement. Soon, (mostly private) stations stopped broadcasting on DVB-T, and now, DVB-T2 is about to be introduced, and of course, it's not backwards compatible to DVB-T, so any DVB-T receiver will be a piece of useless junkTM very soon. Considering the beauty of analog TV, this is sickening. There was black-and-white TV. Then they figured out how to put color into the signal while black-and-white receivers would still decode black-and-white and the new color TV signal, and color TV receivers would decode old black-and-white signals just as well as new color TV signals. Then, they put all other sorts of fancy stuff into the signel (stereo, videotext, ...) and everything was still forward and backward compatible. That's what I call good engineering, even more so if you put it into the context of its time and consider how advanced things were with respect to what was possible with the available technology.