Yellowstone's volcanic and hydrothermal history suggests the potential for various kinds of eruptions in the future.
During the three giant caldera-forming eruptions that occurred between 2.1 million and 640,000 years ago, tiny particles of volcanic debris (volcanic ash) covered much of the western half
Such a giant eruption would have regional effects such as falling ash and short-term (years to decades) changes to global climate.
The most recent volcanic activity consisted of rhyolitic lava flows that erupted approximately 70,000 years ago. The largest of these flows formed the Pitchstone Plateau in southwestern Yellowstone National Park. 
We do not know. Future volcanic eruptions could occur within or near Yellowstone National Park for the simple reason that the area has a long volcanic history and because there is hot and molten rock, or magma, beneath the caldera now.
Contrary to popular belief, Yellowstone was not named for the abundant yellow-colored rhyolite lavas in the Grand Canyon of Yellowstone that have been chemically altered by reactions with steam and hot water to create vivid yellow and pink colors.