What transaction was processed in the beginning? If there were very few coins available and people had to "mine" before they earned coins in the beginning. 

What were they mining if there were no transactions to process? ie. no one had any coins to spend and if you arent spending there aren't any transactions to process to earn points. Seems like a chicken and egg scenario.
Creating blocks without transactions is trivial, valid, expected under certain circumstances, and in fact happens all the time.

There is no chicken-and-egg problem. The first blocks were just empty.