Question

Does DNA replication take place in the same direction along both strands of the DNA molecule that is being replicated?

Answer 1

Yes, if you're talking in terms of 3' and 5' ends.

One strand is replicated away from the replication origin; the other is replicated toward the replication origin.

Answer 2

^ That's correct. During DNA replication of a double-strand there is a leading strand being replicated continuously and a lagging strand being replicated, which is discontinuous where the DNA primase adds on small DNA fragments known as Okasaki fragments.