For example, when Jerusalem fell, how long did it take for the Christians on the other side of the world (ej: London or Paris) to know? Since it was a primitive way of sending messages. (Sorry for my english, still haven't perfected it).
Please don't say primitive. That's derogatory. An essential part of life for the vast majority of people that have ever existed was the experience of only being able to communicate as fast as your legs, horse, or sails could carry you.
It could take 6-12 weeks for a ship to travel from Barcelona to Constantinople, depending on what kind of ship (sailing ship or oared galley), how many places you stopped, and how long you stayed at each stopping point. Weather, pirates, supplies, were a huge factor. A sailing ship could travel from Barcelona to Sardinia and back in something like two weeks; again, an oared galley would be faster. A message dispatched from the royal court in Paris could take anywhere from a 1-2 weeks to a month to get to the King of Aragon, in north eastern Iberia. I draw these numbers from my own research using medieval letters and commercial documents.
According to Goitein's Mediterranean Society, it could take a message 5 days to get from Alexandria to Fustat (Old Cairo); 12 days from Alexandria to Ashkelon (in modern Israel); and 10 weeks from Alexandria to Tunisia.
I'm sorry, but according to reddit there's one comment, however I can't see it. Is it hidden or has it been removed?
Travel times were highly variable. I don't have a good answer, but there's a great resource called ORBIS that will give you approximate travel times across the Roman Empire at different times of the year and by different methods: http://orbis.stanford.edu/ That could help estimate an answer about travel time in later periods.