LED circuit analysis problem
Since you're working with diodes with an AC source it is far simpler to split it into two circuits with different DC sources. First convert the RMS voltage into a PEAK voltage since you are effectively rectifying. \$250V_{RMS} = 707V_{P-P}\$ or \$±353V_{PEAK}\$.

Now make two circuits:







simulate this circuit &ndash; Schematic created using CircuitLab

The purpose of the diode is purely to protect the LED during the reverse voltage phase of the AC supply, so all we need to know is that whatever current flows through it is within acceptable levels (200mA according to the specs). So we just need to solve R1 for the LED and check that the same resistance will be OK for the diode.  So a simple LED resistance calculation:

\$R_1 = \frac{V_S - V_F}{I_F} = \frac{353 - 1.7}{0.02} = 17565\Omega\$

Now feed that resistance into the same formula rearranged with the diode instead (the datasheet just says "&lt;1V" for \$V_F\$ so I will assume 0.7V):

\$I = \frac{V_S - V_F}{R_1} = \frac{353 - 0.7}{17565} = 0.02006A\$

So that value is well within tolerance for the diode. Now, what if I was wrong about the diode's forward voltage? Just out of interest, what would the current be with the diode completely shorted out? Simple:

\$I = \frac{V_S}{R_1} = \frac{353}{17565} = 0.0201A\$

Still well within tolerance.