God Of War 3 shows Athena in spectral form after Kratos kills her in God Of War 2 and later on she gives him blades of the exile. Does this mean that other gods that Kratos killed are alive in some form and can they give their followers weapons and other stuff that might give the gods their powers back?
In GoW 3 Athena says that "her sacrifice to save Zeus has brought her to a higher existance". see cutscene at ~0:30
Also, Zeus had an appearance in his Astral Form in his fight against Kratos. see cutscene at ~18:28
This does suggest that every god might have an Astral Form after death, however these are the only appearances that I know of. According to the wiki it is unclear, if all the gods have access to the Astral Form. But an interesting fact is stated here: Both Athena and Zeus were killed by the Blade of Olympus which might be an indication that this is necessary for an Astral Form to appear. Also we never see an Astral Form of a Titan, despite Kratos killed some of them with the Blade of Olympus.
This is why I think it's not probable that the Greek Gods are alive after GoW 3. It appears however that we don't have all the facts and because of that it remains unclear if that is the case.
I don't think so, because Kratos has slain them all(including the Greek God Zeus), After the execution on Zeus the Greek mythology story is over, and Sony has moved to Norse Mythology.
What happened between God of War 3 and the new Norse mythology is the question here.