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.