What was the first use of the saying, "You miss 100% of the shots you ...
The flow rate increases 100-fold (one hundred-fold) Would be a more idiomatic way of saying this, however, the questioner asks specifically about the original phrasing. The above Ngram search would suggest that a one hundred has always been less frequently used in written language and as such should probably be avoided. Your other suggestion of by one hundred times is definitely better than a ...
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relating to 100 years : marking or beginning a century, with the example "the centurial years 1600 and 1700". But there is a word that is widely used to indicate the range of years or centuries covered by an article or book: history.
You miss 100 percent of the shots you don't take. 1991 Burton W. Kanter, "AARP—Asset Accumulation, Retention and Protection," Taxes 69: 717: "Wayne Gretzky, relating the comment of one of his early coaches who, frustrated by his lack of scoring in an important game told him, 'You miss 100% of the shots you never take.'" ...
As you note, "percent" means "for every hundred," so there is nothing at all wrong with percent values greater than 100 when discussing proportions, e.g. profits increased by 120%. Like fractions, however, percent values are longer to express than multiples, so for values much greater than 100 you may hear them less frequently:
Yes, the correct usage is that 100% increase is the same as a two-fold increase. The reason is that when using percentages we are referring to the difference between the final amount and the initial amount as a fraction (or percent) of the original amount.