What to do when you live in a shoe isn't really a "popular saying" across the world at large. Google finds only 31 instances of this quotated text on the whole of the Internet, at least half of which are simply duplicated references to the same original instances.
A related but far more common expression is living in a shoebox, meaning "in a small appartment". This probably owes much to the nursery rhyme There was an Old Woman Who Lived in a Shoe who had so many children, she didn't know what to do.
OP's (possibly quite localised) idiomatic usage seems to convey a sense of making the best of limited resources. I'm assuming when he gives this reply to someone asking why he doesn't have fast broadband, it's because he lives in a rural location where fast connections are unobtainable or prohibitively expensive.
My own guess is that OP's meaning has arisen circuitously from the original nursery rhyme context. Apart from lacking access to modern contraceptives, the old woman was probably poor, since people living in rural locations are on average poorer than those in the city.
When it comes to broadband, the economics become even more relevant. Even if you live in a tiny apartment in a city, you can probably get cheap broadband because the cost of wiring up the whole building become insignificant when shared between all the people living there. When you live in a farmhouse miles from anywhere, the cost of getting connected by cable can be astronomical.
A potted history is brief, a quick summary. Potted meat is meat, usually not of the highest quality, processed and preserved in a tin. The expression is often used in a derogatory way, as it is in your example.
Let's see... yes, Merriam Webster gives as an example quote under "potted":
briefly and superficially summarized- a dull, pedestrian potted
history — Times Literary Supplement
But, if you were to say, for example, "In the interest of time, I'll just give a potted history of this...", there would be no negative connotation.
This does not correspond to the American "canned", which carries the strong connotation of artificial and stale. "Canned history" would be understood and humorous, but it is not an idiom. In American, "the cliff-notes version" is often used, from a well-known series of booklets for students of brief, condensed summaries of famous texts. This too is often but not always used in some derogatory sense.
Best Answer
Suppose that we believed that an important event divided a century into two parts and those two parts were not of equal length. Examples might be the Stock Market Crash in 1929, Yuri Gagarin being the first man in space in 1961, or Margaret Thatcher becoming Prime Minister in 1979. We then have the century divided into two parts, that are not halves.
If we literally mean the second 50 years (or some approximation thereof), then second half is surely preferable.