Is it good to know archetictual styles for Interior Design? Is it import to incorporate the style into your design?

It is more important to learn the styles from the History of Interior Design. As you learn about details of art, furniture and interiors from various periods in the past, you will also learn about how these relate to the architecture of the time. This isn't knowledge that you need prior to beginning college level classes; any associates or bachelor's degree program should have at least one course in history as part of the curriculum. On the other hand, if this is something that you are particularly interested in, check out some books from the library and start to learn now!

Good luck.