Is the reward for successfully mining a block a transaction on the bitcoin network? If so, what are inputs to that transaction? If not, how are rewards tracked in the network?
Yes, it is known as a coinbase transaction. It is the first transaction in every block and has some slightly different rules to all others. It has blank inputs, can not be spent for 100 confirmations, and can create a maximum of the current reward amount plus the fees collected in that block.