ROC curves plot TPR vs. FPR and vary the thresholds based on the rank order of the probabilities of the training set. The threshold that is picked is the probability associated with the point in the top left hand most corner. That basically maximizes the TPR and minimizes the false positive rate.
However, lets say my application talks about minimizing false negative rate? Then how would this curve change? How about a balance between the two?
It seems to me that you are somewhat misunderstanding what a ROC curve is.
A ROC curve plots TPR vs FPR as threshold is varied. As a result, ROC curves are actually 3-dimensional graphs, plotting the relationship between 3 variables: FPR, TPR, and Threshold. Each point on the graph reflects what the actual TPR and FPR are for a specific threshold value. The lower-left corner of the graph always reflects a threshold of 1, while the upper-right corner reflects a threshold of 0.
ROC curves have two usual uses: to compare two different models independent of threshold, and to help select the proper threshold. The "proper threshold" for a predictive analytics application will vary quite a bit based on the specific problem that you are attacking, but in general, you can use a ROC curve to pick a threshold with an acceptible TPR/FPR tradeoff for your specific application. It is rarely the case that simply picking the threshold for the point closest to the upper left corner will give the ideal outcome.
Once you pick a threshold that seems ideal from the ROC curve, you can investigate the confusion matrix and other evaluation metrics (precision, recall, accuracy, F1, etc.) to assess the threshold further.
To answer your direct question, you are correct that ROC curves don't directly show the FNR. In this case, you may want to use a Sensitivity/Specificity graph, which plots TPR vs TNR in a similar manner to the ROC curve. There is no standard evaluation method that I know of which looks directly at FNR. Instead, I usually just switch the "positive" and "negative" labels in my data and replot the ROC curve. This gives (effectively) TNR vs FNR.