Jews around the world celebrate the holidays, or "feasts" as you call them. However, there are some differences in observances.
Outside of Israel, an extra day is added to each holiday. This means that while the Israeli Pesach is 7 days, it's 8 elsewhere. Also, due to the formation, in Israel it's 1-5-1, where the ones are full holidays (with restrictions on work), and in the middle is "chol hamoed" -- fewer restrictions. Outside of Israel, it's 2-4-2, with an extra holy day added to both parts.
Yom Kippur is only one day worldwide, because it's too hard to fast for two days.
Rosh Hashanah is also two days even in Israel, due to ancient tradition.
This applies to the modern age. When the Temple stood, it was a positive commandment to go up to the Temple on Pesach, Shavuot, and Sukkot. Obviously, not everyone made it.
Also, Erev Pesach (14th of Nisan) there was the korban Pesach (Pascal lamb) to be brought. For those unable to make it (due to distance or ritual impurity), they could make it up one month later, on the 14th of Iyyar (Pesach Sheini).
Hope this addresses your concerns.