Learn English – the origin of the term “crash hot”

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 

The Online Etymological Dictionary says:

To get something under (one's) belt is to get it into one's stomach.

The Oxford English Dictionary says:

Colloq. phr. under one's belt, in one's stomach. Also fig.

Their first three citations are:

• 1839 The Spirit of the Times: Away we went, each bearing, under his belt, his full share of the antifogmatical?compound.
• 1938 A Dictionary of American English on historical principles: Belt, v.? To put under one's belt; to swallow.
• 1954 The Manchester Guardian Weekly: His wife had 135,000 miles driving in the States under her belt?but was still failed.

Here's three earlier literal examples, all about a lot of alcohol under one's belt.

• 1762's The Young Hypocrite by Samuel Foote:

• 1790's The Expedition of Humphry Clinker by Tobias Smollett (first published 1771):

• 1817's Ormond, a tale by Maria Edgeworth: