Learn English – the origin of the phrase “cut and dried”

Here, fast doesn't mean "(capable of) moving quickly". Much rather, it is being used in the sense "firmly fixed" (see fasten your seatbelts or fast friends). The Phrase Finder says that "This is a nautical term. A ship that was hard and fast was simply one that was firmly beached on land." It adds that the term was used in figurative sense by the early 19th century.

Personally, I don't think it's being used more commonly in the negative. Indeed, a quick COCA search returns 40 occurences of "hard and fast rule" or "hard-and-fast rule", but only 22 of them are using it in a negative context — and I am being as generous as possible there, counting not only "no hard and fast rule" and "not a hard-and-fast rule", but also "don't have any hard and fast rule", "rather than any hard and fast rule", "was never a hard-and-fast rule" and the like.

One thing stands out to me, though: out of 16 occurrences of "hard-and-fast rule", with hyphens, 12 appear in a negative context, or 75%. For the non-hyphenated version, it's almost the other way round: 60% positive, 40% negative. (Again, counting "negative" very generously.)

The figures from the BNC are too small to be statistically meaningful. But anyway, here's an overview:

                              COCA                   BNC
                        total   negative      total   negative
hard and fast rule        24       10            8        7
hard-and-fast rule        16       12            1        1 

http://www.phrases.org.uk/meanings/cut-the-mustard.html

There has been an association between the heat and piquancy of mustard and the zest and energy of people's behaviour. This dates back to at least 1672, when the term 'as keen as mustard' is first recorded. 'Up to mustard' or just 'mustard' means up to standard in the same way as 'up to snuff'. 'Cutting' has also long been used to mean 'exhibiting', as in the phrase 'cutting a fine figure'. Unless some actual evidence is found for the other proposed explanations, the derivation of 'cutting the mustard' as an alternative way of saying 'exhibiting one's high standards' is by far the most likely.

Whatever the coinage, the phrase itself emerged in the USA towards the end of the 19th century. The earliest example in print that I've found is from The Iowa State Reporter, August 1897, in a piece about the rivalry between two Iowa towns:

Dubuque had the crowds, but Waterloo "Cut the Mustard"

The use of quotation marks and the lack of any explanation of the term in that citation imply that 'cut the mustard' was already known to Iowa readers and earlier printed examples may yet turn up.