Search:

See DFS tutorial. Actually, you can't speed up DFS to find concrete vertex in the worst-case. Just, when DFS hits the vertex you are looking for, backtrack without visiting other vertices.

The main difference, is that binary tree is a common data structure, but the binary search tree has some "order" in it.

Look binary search tree tutorial for more info.

First, I would recommend you the simple programming tutorials website, where you can find some information on DS. Do you need a more theoretic book or binded to some programming language?