The textbook is Reed's A Balanced Introduction to Computer Science. More details can be found on the information page.
That depends on why you buy textbooks.
If you like to read around a subject, to get additional background, then, yes, buy the book.
If you only buy a textbook because you have to, or because the
instructor says to buy it, then you don't need to. I will post the
slides from my lectures on the web, and those, and the notes you take
in class, should be enough to see you through.
See my notes on submitting homework.