Why is proton coupling through bonds and how does this affect identical protons?
How does a proton create a magnetic field that influences the neighboring protons (mainly) through bonding and not through space?


Through space coupling is known as dipolar coupling and is actually much greater than through bond coupling (J-coupling).  However, in low viscosity liquids the chemical shift effects of dipolar coupling are averaged to essentially a single value by molecular rotation.  Relaxation effects of dipolar coupling are still observed.  


  Why do identical protons not influence each other?


For two protons there will be four states $\alpha \alpha , \alpha \beta , \beta \alpha$, and $\beta \beta$.   In the general case, each state may have a different energy and there can be four possible one quantum transitions ($\alpha \alpha$ to $\alpha \beta$, $\alpha \alpha$ to $\beta \alpha$, $\alpha \beta$ to $\beta \beta$, and $\beta \alpha$ to $\beta \beta$), each transition having a unique energy and hence 4 peaks (two doublets). 

However, when the two protons are equivalent, $\beta \alpha$ and $\alpha \beta$ will be the same energy, $E_2$ let's say.  So, letting the energy of  $\alpha \alpha$ be $E_1$ and $\beta \beta$ be $E_3$, and given a one quantum transition, the possible energies for transtions are only $E_3$ - $E_2$ and $E_2$- $E_1$.  But $E_3$ and $E_1$ are equally spaced above and below $E_2$, so there is only one energy of transition. 

For a more-rigorous explanation see: http://www.chemie.uni-hamburg.de/nmr/insensitive/tutorial/en.lproj/energy_levels.html