i prefer 'burn that bridge...'
do you know the origin of any of them?
translate: will you do the homework for me?
I'll give it a try but don't have much time to research:
Burn that bridge - based on the military action of burning a bridge you have just crossed to prevent the enemy from crossing it after you.
Hit the nail on the head - No one knows the exact origin of this phrase. What is known is that it is extremely old. It appears in The Book of Margery Kempe, circa 1438. This was an account of the life of religious visionary Margery Kempe and is considered to be the earliest surviving autobiography written in English reads as:
"If I hear any more these matters repeated, I shall so smite the nail on the head that it shall shame all her supporters." Today, we simply use this idiom to mean that something is precisely right.
Cross that bridge when you come to it - Deal with a situation when, and not before, it occurs. The ultimate origin of this proverb, a caution not to anticipate trouble and often put as don't cross a bridge till you come to it, has been lost. The earliest recorded use is in Henry Wadsworth Longfellow's The Golden Legend (1851): “Don't cross the bridge till you come to it, is a proverb old and of excellent wit.”
Kill two birds with one stone - The phrase appears in a 1632 book by J. Morgan Gent and a 1655-1656 exchange between Thomas Hobbes and John Bramhall. Though its precise origin is unclear, the earliest English appearances of the phrase date back to the 17th century.
An arm and a leg - 'It cost and arm and a leg' is one of those phrases that rank high in the 'I know where that comes from' stories told at the local pub. In this case the tale is that portrait painters used to charge more for larger paintings and that a head and shoulders painting was the cheapest option, followed in price by one which included arms and finally the top of the range 'legs and all' portrait. As so often with popular etymologies, there's no truth in that story. Painters certainly did charge more for large pictures, but there's no evidence to suggest they did so by limb count. In any case the phrase is much more recent than the painting origin would suggest.
Cist an arm and a legIt is in fact an American phrase, coined sometime after WWII. The earliest citation I can find is from The Long Beach Independent, December 1949:
Food Editor Beulah Karney has more than 10 ideas for the homemaker who wants to say "Merry Christmas" and not have it cost her an arm and a leg.
'Arm' and 'leg' are used as examples of items that no one would consider selling other than at an enormous price. It is a grim reality that, around that time, there were many US newspaper reports of servicemen who had lost an arm and a leg in the recent war. It is possible that the phrase originated in reference to the high cost paid by those who suffered such amputations.
A more likely explanation is that the expression derived from two earlier phrases: 'I would give my right arm for...' and '[Even] if it takes a leg', which were both coined in the 19th century. The earliest example that I can find of the former in print is from an 1849 edition of Sharpe's London Journal:
He felt as if he could gladly give his right arm to be cut off if it would make him, at once, old enough to go and earn money instead of Lizzy.
The second phrase is American and an early example of it is given in this heartfelt story from the Iowa newspaper the Burlington Daily Hawk-Eye, July 1875:
A man who owes five years subscription to the Gazette is trying to stop his paper without paying up, and the editor is going to grab that back pay if it takes a leg.
Other cultures have similar phrases; for example:
In France - Ça coûte les yeux de la tête - It costs the eyes from the head.
Bulgaria - Това струва майка си и баща - It costs one's mother and father.