At a construction site, in order to maintain uninterrupted progress and timely completion of the project, workers are split into two shifts as 'day workers' and 'night workers', enabling operations to continue 24 hours a day. Day workers are paid at a rate of \(₹\) \(350\) per day, while night workers are paid \(₹\) \(620\) per day.
Based on this information, answer the following.
1. If the total wages paid by the project engineer is denoted by \(c\), then represent the given situation in the form of a linear equation in two variables.
2. If there are \(13\) day workers and \(6\) night workers are working on a particular day, determine the wages paid for that day in rupees?
3. If no night workers were employed for the day, then how much total wages did he pay for the \(13\) day workers in rupees?
4. If no day workers were employed for the day, then how much total wages did he pay for the \(6\) night workers in rupees?