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.
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 ...
"100%" is equivalent to "all". There is no rounding with "all"; either you get all of something or you don't. If a product advertised itself as "kills all bacteria" and then you found that there were 3 bacteria that it didn't kill, it doesn't matter whether that's 3 out of 10 or 3 out of 28 million; it's not all of them. Even in ordinary conversation, if your child says "I picked up all the ...
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.
Numbers with more than 100 zeros - English Language Learners Stack Exchange
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:
37 Wikipedia lists large scale numbers here. As only the 10 x with x being a multiple of 3 get their own names, you read 100,000,000,000,000,000,000 as 100 * 10 18, so this is 100 quintillion in American and British English and 100 trillion in most (non-English speaking) other places.
The type of writing you are doing also plays into your decision. For example, in legally binding documents, like contracts or exhibits to contracts, the spelled out number is the legally binding number. So if a text said that, "you are 99% (one-hundred percent) responsible", the 100% number would be legally binding, not 99%.