Relation between Network Hash-Rate & bitcoin value? how is the relation betweeen network hash rate to healthyness of bitcoin, such as bitcoin value compared to USD, or the growth rate of this currency?
You can find graphs charting this relationship at http://bitcoinx.com/charts/. (scroll down)

Network hash rate and exchange rate are certainly correlated, but the relationship is very complex, I think it would be inaccurate to say that one depends on the other. In general, if price increases due to an outside factor (eg. new adopters buying Bitcoins) hash rate will go up, as you can see in the chart at the above link around July 2011, when price spiked and hash rate followed.

Impact of hash rate changes due to outside factors on price is harder to predict. Hash rate increases can lead to increased investor confidence in the currency (which would increase price), but they can also drive miners on the edge of profitability out of mining and potentially even Bitcoin, decreasing the price. (less participants in a market generally leads to price decreases, though not always)