In aircraft operating in a maritime environment, corrosive effects from salt water are common. Are there any specific coatings used in engines for such aircraft? If so, which are they? How frequently should they be washed? I've looked for information on this but can't find any specific answer.
Not aware of any anti-corrosion coatings used in engines. The best mitigation is to shoot fresh water into the inlet with it running at the end of the day. Seaplanes operating off salt water will generally get a fresh water hose down at the end of the flying day whenever practical.
There are different metallurgical mixes that react more or less violently with seawater, and the Russians were, and are, very good at that, not least Beriev, so their engines are made to operate near seawater, thus need to have different metals used internally, compared to ordinary engines.
As we all know a lot differs between an RAF Harrier and an RNAF Harrier, not least due to their different operating milieu, like the plating used internally. And I guess the same applies to various models of the F-35?!
I do not know anything in detail, but might be available. Magnesium is avoided in a salty context, lithium-aluminum works well (if my memory serves me right), as does Alclad.