Will the block chain ever become too large?

Does every Bitcoin instance on a peer node download this entire block chain? 

At this time, yes, every bitcoin app downloads its own copy of the full block chain.

This is not absolutely necessary. Several levels of optimization are available; it's just a "simple matter of programming".

In the future, big nodes (e.g. those operated by exchangers) will download the whole block chain, but the "average joe" will run a "bitcoin lite" that just downloads the data needed to support his own use of bitcoin.