By which time can we collect on ship chandlers and Bunkering claims in Greece ?

By the end of the year starting as of January 1st of the year next to the one during which the supplies/bunkering were provided to the vessel.

What is the appropriate court in Greece to sue for shipping claims ?

All such shipping claims in the Attica area are adjudicated exclusively by the admiralty divisions of the Piraeus  first and second instance  courts. However, even if the venue of the case stays before any other  court in Greece still the said admiralty divisions of the first and second instance  Piraeus courts have concurrent jurisdiction which means that we can sue before the said Piraeus courts no matter whether the shipping claims were born in any other part of Greece, i.e. Pylos, Crete, Salonica, Corfu, etc.

What is the outcome of shipping claims ?

In most cases such claims are collected by an amicable settlement after you agree to wipe out the interest. In all other cases the outcome depends, among other things, on whether such claims have been time barred or not as well as whether your adversary will go with the court all the way or not.