Why the OFDM symbol length is the total number of original modulated symbol, but not one symbol length?
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.