Also where do most architects get inspiration? How can they just whip up a brilliant plan in like a day?
No worries - you are the perfect age to pursue architecture and become an architect.
While it is true that some individuals learn of their desire to become an architect at an early age, just as many learn of their passion at your age or even later. Philip Johnson, one of the most influential 20th century architects did not pursue it until he was 39 years of age.
Philip Johnson - Glass House (1949)
Trust me, you are not too old -- pursue it with a passion.
As for inspiration, it varies but one of the most important skills of an architect is "to see." As you go through your daily life, SEE your surroundings. Look at the built environment around you and take mental notes -- look at nature, people, materials. All of it becomes inspiration.
As to your last question, they do it because they have an architectural education and experience, something that you will pursue. Also, read architecture books as you have and even websites that highlight architecture to gain inspiration.
Finally, draw and sketch to express your ideas.