No. In a simulation program a battery is considered to be a perfect voltage source, so the output would be V2 with or without the FET. When you run the sim what does it show?
No, it creates a constant current source that only conducts when the instantaneous voltage from the AC voltage source is sufficiently high enough compared to the battery voltage to allow the JFET to generate enough current to cause the JFET to pinch off. Just noticed that your AC source is only 1V, there are few JFETs that will pinch off at such a low voltage.
No. In a simulation program a battery is considered to be a perfect voltage source, so the output would be V2 with or without the FET. When you run the sim what does it show?