It looks to me like your second formula is still incorrect. You should keep the two currents going in the same direction. The first current is clockwise (although its easier to keep the signs straight if you go counter-clockwise in this case) so you get -2A as you said. In the second case...
I would begin by assuming that D1 is conducting. If D1 is conducting then you immediately know the voltage across R2 since the voltage across an ideal diode is constant. From there you can calculate the current in each node. If D1 is not conducting, then the resulting currents and voltage...
Sink current means current going into the voltage source. Source current means current going out of the voltage source. The node I am talking about is the point where the voltage source and current source meet. A current source will force 3A and put no constraints on the voltage. Likewise...
That would be true if the 20V supply was not there. But being an ideal voltage source, it will sink or source current in order to keep the node at 20V.