Do exchange rates between countries' currencies have an influence on Bitcoin exchange rates? Are the exchange rates of each country a factor in the worth of a Bitcoin? Is the use of Bitcoin similar to traveling to another country and having a exchange rate between paper monies?

Basically, are bitcoins affected by the exchange rates of each country or the web exchange?
Bitcoin follows very closely to USD and RMB, because US and China are the biggest players in the bitcoin market now. You can see the trade charts here: http://bitcoincharts.com/charts/volumepie/

Hence US and China exchange rates will affect the worth of Bitcoin. 

In regards to travelling, the merchant accepting Bitcoin will list prices in their local currency. If you pay with Bitcoin, they will use the exchange rate found on one of the exchange networks (e.g. mtgox)