It’s not at all surprising that the origin of the idiom “bend over backwards” is in gymnastics. The term was used as early as 920 CE to compare the athletic act of back bending with an expenditure of effort to ensure that something went as planned. (source)
Today the term has a slightly different meaning. It is usually used to describe accomplishing something difficult for someone and receiving no gratitude, recognition, or even in some cases acknowledgment for it.
I couldn't find an origin for this phrase, I'm guessing it came into being over time. It means that a person is immovable in their behaviors, opinions, beliefs, etc. There are pros and cons to being set in your ways but it is usually meant in a negative way.
Beware of being set in your ways - God can and will change it up. (Proverbs 16:9)
The most interesting theory I found about the origin of this phrase was it popped up in the 1870s when slaves would hold dances mocking the mannerisms of their masters. The couple who won the contest would get a cake as their prize. Thus the dances became known as "a piece of cake" because it was so easy to mock their masters and win. HA! (source)
So today when someone says, "That's a piece of cake" they are referring to the ease of which something can be done.
There's three options for this phrase and the most popular one seems to be about restaurant servers. Diners' wait-staff would get hopelessly behind and overwhelmed by orders, causing them to struggle as if they were walking through remarkably high weeds. Read about the other two thoughts on the phrase here.
Today the phrase has expanded to mean, in general, to be overwhelmed. I actually use it quite a bit.
One theory on the origin of the phrase is that derives from the use of handbaskets in the guillotining method of capital punishment. And it seems that theory is pretty accurate from other accounts. Read more about it here.
The phrase means something is rapidly deteriorating and/or is on course for disaster.
The word Ham to mean an "overacting inferior performer," apparently dates from about 1882 and originates from American English. Originally the word was hamfatter, meaning "actor of low grade," and has been linked to an old minstrel show song, "The Ham-fat Man" which dates from about 1863.
Today when people ham it up they deliberately exaggerate their emotions or movements.
Around the beginning of the 20th century this idiom, and its variations, started appearing in conversation and print. It's meaning is rather clear - even if I were dead I wouldn't be caught...engaging in that activity, wearing that item, doing that thing, saying that, engaging with that person, etc. (source)
Cows are notoriously languid creatures and make their way home at their own unhurried pace. That's certainly the imagery behind 'till the cows come home' or 'until the cows come home', but the precise time and place of the coining of this colloquial phrase isn't known. (source)
These days the phrase is used to indicate something is taking a long time to happen or something will happen indefinitely.
Benjamin Franklin has been credited with the origin of this idiom in some places but it actually showed up in the 17th century, in George Herbert's Outlandish Proverbs, circa 1633: A penny spar'd is twice got.
It's meaning hasn't changed through the years and is quite clear, it is as useful to save money that you already have as it is to earn more.