Increasing current draw of generator receptacles within total generator head rating
The generator you have is called a split-phase generator It is actually a single phase generator) and it's very much like having a center tapped transformer for output: https://en.wikipedia.org/wiki/Split-phase_electric_power



V1-N is 120 V @10.8 Amps
V2-N is 120 V @10.8 Amps  

This gives about 2600 Watts total power.

OR.....
V1-V2 is 240 V @ 10.8 Amps for a total power of about 2600 Watts.

OR....
Any combination of 110 V and 240 V current draws that do not exceed about 2600 Watts total. 

So to answer your question the windings are rated at 10.8 Amps maximum ....but for a short time the generator can sustain a 2900 Watt peak, or 12 Amps through the winding. The limitation here is not actually the winding current limit but the magnetic regulation that will cause the output voltage to drop (and hence the current will drop).
You CANNOT connect together the two 110 V outputs since they are not in phase. It would be like joining together the two output wires of a center tapped transformer. In the transformer case you'd burn it up, but in the generator case the output voltage would collapse (though it may eventually damage your generator if you left that short in place).