We need to knock some sense in your head. I'll try.
You should not input a sine wave current source and look at the DC out.
Since this circuit is expected to amplify AC, the output will be DC+AC and be the right output if the probe is DC coupled.
The circuit does respond to DC, so use a DC current in and measure a DC voltage out at -2.5mA, 0mA and 2.5mA.
In the real word, there is an input offset voltage which also gets added to your DC value at the + input. So, zero V in wont give you the expected value. I have no idea if that shows up in simulation.
You do need to put a capacitor across the feedback resistor, it's a real word requirement. You should see the effects in simulation.
Good old fc=1/(2*PI*R*C); Fc is the -3db frequency. The output is down 70.7% at that frequency. Fc has to higher than the frequency of interest.
Real world requires bypass capacitors, but you don't need them in simulation.