Can I earn transaction fees by running as a full node, verifying transactions, but not mining? As I understand it, by running a full node (i.e. Bitcoin-QT) , I am helping confirm transactions and contributing to the Bitcoin network. 

When transaction fees are offered, do I receive these, and if so, how? Or do I need to be a fully fledged miner?
Nope, transaction fees of a transaction can only be collected by including it into a valid block. And to be able to include a transaction in a valid block you have to mine a valid block.