1. Where do you want to use 50Ohm? In |Zout| simulation? Not recommended. I don't understand this question actually.
2. When you measure |Zout| of your circuit you actually measue |Zout + Xc|, where Xc is the added capacitor's reactance. To keep this Xc part low, especially at low frequencies, you have to use large capacitor because Xc = 1/(2*pi*f*C).
3. When you simulate in DC a non-linear circuit the AC field of the vdc source is not important. But if you simulate AC, you want to know how is your circuit AC transfer function in a DC operating point. vdc source has got an AC field, because in AC simulation we don't want to change any source, just type in an AC magnitude where it is necessary.