I think all you really have to consider is the current in the 10k load resistor. This current adds or subtracts from the standing current in the diodes
Start off by considering the circuit when Vin is zero. The current through each diode is 0.5 I. There is no current in the voltage source or the load.
When Vin is non-zero, a current is forced through the load resistor. This un-balances the current in the diodes.
Don't forget that the current sources have infinite impedance. This means that, in your circuit, the earth point has no relevance. It could be drawn as a series connection of the voltage source and resistor across the diode bridge. The current through the load resistor will always equal the current in the voltage source.
The current source(s) appear to bias the diode network. The estimation of current flow across the diode network from the small signal source to the 10k resistor would presumably take into account the dynamic resistance of the diodes at their bias condition. Conduction across the diode network would not be possible in the absence of the biasing - given the diode orientations.
I'm not sure what this problem is all about - i.e. what is the context? I've "guessed" it's got something to do with dynamic resistance. Maybe signal modulation / multiplication?
The absence of any information about what assumptions can be made is also a little disconcerting.
Part (c) makes some sense since the peak current in the resistor was ~0.1mA (10% of the bias current). The (more accurate) source voltage required was ~2.019V peak-to-peak. This makes the drop across the diode network about 19mV peak-to-peak.
It was difficult to set up a solution for part (b) but I have a value of I=70nA. Vout was about 140uV peak-to-peak.