No, disease names are not proper nouns, although diseases named after people keep the capitalization of the person's name (Münchausen syndrome). The scientific (Latin) names of disease-causing organisms follow the standard rule of Genus species.
If you've seen "Celiac Disease", it's just because of an unfortunate tendency some People have to capitalize Random Nouns as if English were half German.
Don't think of Australian dollar as a single proper noun. Instead, think of it as a combination of two words, meaning "a dollar that happens to be Australian":
Australianproper adjective + dollarcommon noun
There are lots of kinds of dollars, and we use adjectives like Australian and Canadian to say which sort we're talking about more specifically. There are lots of kinds of rupees, too, and we use adjectives like Indian or Indonesian to specify which sort we mean. Something similar is true of the Japanese yen and Chinese yuan (which are, by the way, etymologically the same word).
Note that in the preceding paragraph I talked about kinds of dollars and kinds of rupees. I didn't just say dollars and rupees, because an individual dollar is a piece of currency! If I have five dollars, I have either five one-dollar bills or I have some other denominations that happen to add up to five dollars. There is no singular dollar—there are many dollars!
Even if the US dollar were the only dollar in existence, the word dollar still wouldn't uniquely identify a single entity. And the same is true of the word cedi. If I have two cedis, I have two hundred pesewas. There is no singular, unique cedi to which the word refers. So semantically speaking, we have no motivation to treat the word as a proper noun. And syntactically, we don't: I can say a cedi or three cedis, just as I can say a dollar or three Australian dollars.
Ultimately, even if it made sense to treat cedi as a proper noun, the fact is, we don't use it like one, so it isn't one. Any additional explanation is just icing on the cake.
Best Answer
Nordic isn't used a noun in a phrase like "Nordic skiing", it's an adjective. One might call it a proper adjective and it's always capitalised.
OED has
Adjectives which are derived from proper nouns always retain their capitalisation, which is why Scandinavian is capitalised in the OED definition.
Having said "always", there are always exceptions to a rule! I know of only one apparently-proper word which should not be capitalised: english in a very specific sense of spin on a billiard-ball. Normally that's an adjective and should be capitalised; and english as a lower-case noun was probably derived from English anyway, so it wouldn't be a capital offence to spell it with an upper-case letter.