As you say, an ideal op-amp can be considered to have the two inputs at the same voltage, also, it takes no current to drive it.
In your case, the + input is connected to ground so the - input will be at a similar voltage (plus op-amp noise).
The - input will then look like a ground and to drive the amp, you need to put in a defined current. I suggested 1k so that 1V on the input will give 1mA in to the virtual ground.
Since the op-amp takes negligible current, this has to be provided by the 5k feedback resistor, giving 5V at the output.
The waveforms look to be reasonable, you would not expect your phone to behave like a good signal generator. The waveform that you have drawn by hand looks like a differentiated version of the other one, caused by insufficient capacity at the input, cutting the lower frequencies.