The large intestine generally has the patterns listed for it on our tcm diagnostics page. While not conclusive that is most of the common treated patterns.
The terms tonify and balance can be in some situations exchangeable and in other situations entirely different things. In general tonification is exactly what it means - you strengthen the function of the organ system you are tonifying. Whether or not that will ameliorate the patients issues or not depends entirely on how keen your diagnostic skills are and how well you chose your points, herbs, etc. Generally you are looking for the deepest cause and treating that, rather than the myriad manifestations of the imbalance. The better you do that, the more things resolve once the root is balanced.
As you get into yin and yang I would suggest you read our yin and yang theory section first. But in basic terms you are strengthening either the yin functional aspects of a system (it’s downregulating strength, it’s water, it’s ability to cool) or the yang functional aspects of a system (it’s upregulating strength, it’s fire, it’s ability heat and move).