compoundsvocabularyword-usage
Don't be a scaredy cat.
What does scaredy mean in the given sentence? Can I use it singly or is it always paired with cat?
Does it refer to someone who is a coward or is shy? That is, would it be correct to say that "he is a scaredy cat"? And is it considered impolite or offensive?
As commented by @Walter, in OP's context, fancy is a synonym of imagine, believe. But the usage is becoming increasingly "dated"...
Many of the above instances will be the idiomatic exclamation "Well, fancy that"! (equivalent to "Imagine that!", "What a surprise!", "How strange!", etc.). In OP's context, Dumbledore could quite naturally have used any of those (possibly preceded or followed by something like "I didn't expect to see you here!").
Note that Dumbledore is an elderly British schoolmaster in a relatively "formal" situation (he's greeting Professor McGonagall, one of his staff who apparently happens to have adopted the form of a cat).
Idiomatic expressions as used by Dumbledore won't necessarily be so natural for younger speakers, and per @StoneyB's comment below, even Dumbledore is speaking ironically here. Brits in particular still use fancy = like, want, be attracted to quite naturally today, but fancy = imagine, believe, think is now largely confined to ironic/sarcastic contexts.
It does indeed mean no, and this isn't even just "Hagrid-speech"; nah is a common informal way to say "no".
I'm not sure where you mean it should have been placed in the previous sentence, but I'll attempt to explain why it appears where it does.
They didn' keep their gold in the house, boy! Nah, (the) first stop fer us is Gringotts.
There's an implication there in the nah that's based on prior context."The gold isn't in the house; there's no reason to go to the house. No, that's not where we need to go; the first stop for us is Gringotts!"
Basically in this case, the nah is being used to say "No, not that thing you just said. We're doing this." Another example:
Amy: "Did you try that new Italian place on your date last night?"
Mary: "What, and completely ruin my diet? Nah, Mark took me to a sushi place instead."
Best Answer
Thus, it is used with the word cat attached to it.
Though, there has also been another cartoon titled Scaredy Squirrel, but it still isn't used for the phrase.
Yes, it is used explicitly to depict someone as timid or refer to someone who is afraid/coward. I'm not sure that it is applicable to one's shyness too.
Your usage of
scaredy-catin the followingis perfectly correct. Yes, it isn't polite to call someone a coward; but it is correct.