How much of category theory should I know to view schemes, sheaves and cohomology concepts as concrete cases of abstract categorical concepts? Is there a textbook of category theory for AG people?
Paolo Aluffi's Algebra Chapter 0 develops abstract algebra using Category theory from the very beginning. The exposition is very clear and teaches upto and including the derived functor approach to cohomology. The category theory developed here should be more than enough to study sheaves and schemes eventually.
In an answer to your earlier question, Julien Puydt points to (and I second his suggestion) the excellent text by Ravi Vakil. The category theory developed in this text is really all you need; in fact, there is no more than what is needed for purposes of getting started with AG.
These are the first and the second of three volumes on algebraic geometry by Kenji Ueno from AMS as Volume 197 in the Translations of Mathematical Monographs series.
(1) Algebraic Geometry 1: From Algebraic Varieties to Schemes
(2) Algebraic Geometry 2: Sheaves and Cohomology
The answer to your first question "how much of category theory..." is partly that it is a matter of taste. Some people use a lot, while others don't. But, if you plan to study schemes, it is necessary to know some. For example, the product of varieties can be treated naively, but for schemes it definitely needs to be understood in a categorical sense. For existence, it helps to the know that the category of affine schemes is equivalent to the opposite of the category of commutative rings. Many schemes can be understood best in terms of the functor it represents etc. etc.