If I have a Java HashSet<Double> with a length ranging from 1 to 10.000, are the hash codes of this set and all of its subsets unique?
No. Object.hashCode() method implementations (e.g. HashSet.hashCode()) are not guaranteed to return a unique value, only a pseudo random value which is good enough for purpose of hash data structures.
If you nee a unique value for HashSet<Double> based on the set content you should implement it yourself.