I find it interesting that there are many different alphabets across the world yet (to my knowledge) all countries use the same set of numbers. Why is this, and when did it spread across the world?
This is not actually the case. China and Japan both have their own systems of numbers that are still used to this day distinct from Arabic numerals. A number of isolated cultures around the world also use different sets of numbers, some of which are not even base 10.
Also you need to be aware that although we call the standard western numbers "arabic numerals", they are not the same as those found in many Arabic countries, which use totally different numbers. Some Arabic-speaking countries do use western numerals, but many do not.