I have two questions: What is the effect of NO_x and SO_x in controlling the burning zone temperature and what other parameters like kiln torque, kiln inlet oxygen or if anything else affects the kiln operation.
Secondly, how to improve the ventilation in ball mills, as we observe the coating formation on the balls is on the high side.

NO_x and kiln torque are both good indicators of the temperature in the burning zone of the kiln. This is key to ensuring stable operation and good combination of the clinker. Kiln inlet oxygen is a good indicator of the combustion conditions in the kiln where a small excess of oxygen is necessary to ensure burning in oxidising conditions. SO_x rises if there is reductive burning and CO present in the burning zone therefore this reinforces the kiln inlet oxygen measurement.
To improve the ventilation in the ball mill you need to increase the speed of the induced draft fan. However if you are suffering coating of the media this is more likely related to temperature control in the mill. This is a function of the clinker temperature, ventilation and the cooling with water injection.

We have a small three-chamber cement mill, size 2.4m dia x 10m length, grinding ordinary Portland cement clinker. Mill diameter on liners is 2.30m. The mill is working in closed circuit with a mechanical separator, which has a diameter of 4.0m and is equipped with the main and auxiliary fans and distribution plate driven by a variable speed drive motor. The separator uses its own circulating air. The mill circulating load is 275 per cent. The mill output is 12tph at 2900cm₂ /gm Blaine. Total grinding ball charge in the mill is 50t. Separator efficiency is 37 per cent. We want to know if the mill output and Blaine can be increased or is it the maximum for mill of this size. Secondly, is the mill tube L/ D ratio at 4.16 too high for closed circuit operation. Will this mill give higher output if used as open circuit mill?

I do not think you can achieve any more output with a mill of these dimensions. I also don't think that operating it in open circuit will increase the output. In fact 12tph is significantly better than I would expect for a mill of these dimensions.