Electric motor can develop more than 100 HP, but the battery is limited in it's output to some lower number which at the moment escapes me. Therefore , depending on the throttle position the computer will decide at what point it needs ICE to start , to help the battery. Getting going from dead stop is usually high current affair and ICE will come on most of the time, especially during the turn which requires more effort than straight line acceleration.
Fully charged battery can provide higher amperage than lower charged battery: To begin with fully charged cell will have higher voltage and higher voltage will provide higher amperage (everything else being equal) and power is voltage multiply amperage. Anyway:
1. yes, it's normal
2. Ohm laws, see above plus possibly some other things like temperature, computer programing
3. EV limit is about 42-43 miles per hour indicated, but you can run electric only at higher speed, the engine will spin but injectors are cut off from delivering fuel. The reason for the limit is that at higher speed with ICE stationary electric motor that starts ICE runs at too high speed and would have problem to crank the ICE if it was required for more power.
As he said, the indicated speed is higher per agreement by about 2-3 miles (but only above 20 miles per hour, believe it or not bellow 20 MPH the speed is correct). One reason for the agreement I can think off is simple: No instrument is exact, especially mass produced and being used for 5-10 years so if you start on the high side there is very little chance to show the speed lower than actual and if the speedo was showing lower than actual I can see the lawsuits coming with every accident where speeding is a factor. Here, the speedometer shows higher speed than actual, so there is no excuse if you get a ticket or wipe out, fault is yours not the car.