Analysing diode and resistor circuit
Voltage across parallel circuit (R1, D1 in parallel) equals to voltage drop across R1. If the voltage drop gets to 0.8V, current will start flowing through D1 so the voltage drop across R1 will not increase anymore.
So Vin-Vout is either voltage drop across R1 or 0.8V maximum. But this is V1 minus Vout, not Vout itself.
If D2 is open-circuit, there is no current flowing through the R1 and D1 in parallel). Voltage drop across R1 is zero, so Vout equals V1.
If for example, V1 is 10V, Vout will also be 10V (there is no current flowing through R1, so there can not be any voltage difference). Voltage across D1 is still zero.
The &quot;not exactly zero&quot; from your simulation is probably because there is some small but nonzero reverse bias current flowing through D2, that also flows through R1 and creates a small voltage drop.