With a syllable-timed language, each syllable gets roughly equal time. Therefore, the more syllables, the greater the amount of time to complete the sentence.
With stress timed languages, unstressed syllables are dramatically shortened, and typically only key content words are stressed, so the number of syllables doesn't really affect the amount of time to complete the sentence. A sentence with 10 syllables might take the same amount of time as one with 20 syllables, because even some of those one-syllable words won't be stressed.
Yes, Italian is a syllable timed language, as are French and Spanish. English, Swedish, and German are stress timed. All of these use a Roman alphabet. You can't make the assumption that a shared alphabet necessarily reflects a shared stress relationship.
The Hangul alphabet is unique, because it's an artificially constructed writing system designed from the ground up to promote literacy.
As you know, prior to the invention of Hangul, Korean used a mix of several different writing systems,including Classical Chinese, plus several other native phonetic scripts. The resulting mix was a terribly complicated writing system that required lengthy study to master. Hangul keeps some aspects of Chinese writing (i.e. the idea that a character includes a guide to pronouncing the syllable), but wiped the slate clean with simplified strokes that represented sounds only (whereas Chinese symbols also held clues to morphological meanings as well). Thus the axiom of an intelligent man learning Hangul before noon, and a slow man still able to learn it within a few days.
Korean is an example of a true, "pure" alphabet - one letter for each sound. Although we refer to the Roman system as an alphabet, it's not a true alphabet for English because we don't have a letter for each sound. English has around 44 sounds, but only 26 letters to represent them. That's because we've adopted the Roman alphabet for English, which absorbed more sounds from other languages, whereas the original Roman Alphabet was just for Latin sounds.
In some aspects, writing English today is somewhat like writing Korean prior to Hangul. However, at the time Hangul was invented and implemented, there was a relatively small population to mandate the change upon. Imagine trying to introduce a English writing reform in this day in age across how many different nations?