How can dna sythesis occur in both directions from a replication origin

at the replication fork, you have 2 DNAP's. One is on the leading strand and the other is on the lagging strand. Now you into a problem of DNAP's not moving in sync with each other. The synthesis on the leading strand is much faster than the lagging strand because the lagging strand needs to make an RNA primer and then extend the primer (okazaki fragment synthesis/maturation). So DNA synthesis will not be complete on one of the strands.  

There is a model that explains what happens during DNA replication. The model is called the Trombone model.  

You have 2 DNAP's linked together by a tau protein (2 tau proteins) and both tau proteins are bounded to beta clamp loader. This makes the holoenzyme complex.

a- all cells come from pre-existing cells