How can two photons with different frequencies created by parametric down conversion be indistinguishable? We have two photons created by the same four wave mixing process. How are they indistinguishable if they have different wavelengths? I know that as they are created at the same moment by the same process, they are indeed entangled, but I cannot understand how they have different wavelengths and they are indistinguishable at the same time.
 A: 
We have two photons created by the same four wave mixing process. ... they have different wavelengths.... I know that as they are created at the same moment by the same process, they are indeed entangled,...

In your case, it is obvious that the knowledge about the frequencies of each photon is unknown to an observer as long as the frequency of one of the photons is not measured. At that moment, the uncertainty (function) - which photon has which frequency - collapses. The result is unambiguous.
Another result of a well designed parametric down conversion are photons of the same wavelengths but entangled spin orientations. To prove the entanglement is more difficult because the spin orientation could be any value in the range of 360°. To measure the spin one use a filter which let photons in the range from say 0° - 90° and 180° - 270° through. So in 50% a photon with randomly orientation of his spin is blocked. To prove the entanglement one has to carry out the measurement on more than one photon pair and only after a lot of measurements the correlation occurs from which we conclude than about the strong entanglement.

How can two photons with different frequencies created by parametric down conversion be indistinguishable?

They are indistinguishable as long as nothing is measured. After the measurement of one of the photon, the result for the second is known without measurement. BUT this is right only for a process (the parametric down conversion) for which the production of photons with two wavelengths is well designed. Because it could be that the process changes under temperature influences. So you will be sure about the entanglement only for a well designed setup.
The difference between the collapse of the uncertainty about the result for spin entanglement and for frequency entanglement is the next. The frequency entanglement is a binary system, the spin entanglement is a fifty-fifty process and only after many measurements with always the same setup of unchanged in their orientations filters a correlation occurs which gives the knowledge about the entanglement.
Your example is brilliant. It shows that the discussion about spooky action at distance (spukhafte Fernwirkung) could be terminated. Simply the particles are from the moment of creation in an unambiguously state and it is obvious that the measurement of one particle gives us the knowledge of the state of the second.
