How do multiple replication forks function without 'colliding', and what is the benefit of this method?
To get to the exponentially increasing number of strands, the replication would have to be started on the already replicated strand, and not on the original strand. Replication in eukaryotes is tighly controlled and such an event is prevented by the regulation.

How can the cell prevent re-replication of the strand that is currently synthesized? By timing the steps of the replication in strict order and preventing any replication outside of that order. 

Replication starts at defined origins of replication. In the G1 phase, pre replication complexes (pre-RCs) are assembled at the origins of replications. At these pre-RCs the replication can be initiated, but pre-RCs itself cannot be assembled in the later phases of the cell cycle. When the replication starts, the pre-RC is converted to a post-RC which can't initiate the replication anymore, preventing re-replication.

The benefit of multiple origins of replication is replication speed. Eukaryotic genomes can be much, much larger than those of simple bacteria. Replicating them using a single origin of replication would take a very long time.

Some further reading material:


Genomes, 2nd edition, chapter 13
Cell Cycle Regulation of DNA Replication