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 ...
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.
2 Use 100% when you are stating mathematical thought like statistics. Use "one hundred percent" when you are stating non-mathematical thought like a story.
24 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.
People often say that percentages greater than 100 make no sense because you can't have more than all of something. This is simply silly and mathematically ignorant. A percentage is just a ratio between two numbers. There are many situations where it is perfectly reasonable for the numerator of a fraction to be greater than the denominator.
All of your variants are grammatically correct, and will be easily understood by native English speakers. The less than X is idiomatically identical to under X when referring to monetary amounts, as is more than X with over X. However, if your audience is international, you might prefer to say items costing less than X or items costing more than X simply to avoid any possibility of confusion ...
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.'" ...
In a scientific or mathematical context they might occur, in which case you should use standard index form 1×10¹⁰⁰ for one followed by 100 zeros. There is the joke word "googol" for this.
If soap A kills 100% and soap B kills 99.99% of bacteria, the remaining amount of bacteria after applying A (0%) is infinitely smaller than the remaining amount of bacteria after applying B (0.01%). Therefore A is much, much better. You can see from these examples that 0.01% gap behaves differently across the percentage scale.
