Can the mass flow rate for different power settings be determined? Is it possible to determine the mass flow rate for different power settings? Unfortunately I was unsuccessful in finding the engine specification for the PW2037 so I used the data from this source, which states that the mass flow rate at take-off for the PW2037 engine is 1210 lb/s. Given this flow rate, would it be possible to calculate the mass flow rate at idle setting? And therefore also the mass flow rate for 50% engine setting (or 25%, 75%, etc.)?

An answer in this question suggests using thermodynamic equations to approach this. However, I am not too sure on how to use these equations.
Yes, it can be done but you need a complicated model with information only the producer has access to. The data in your source are not enough.

You can play around with this a bit https://www.grc.nasa.gov/www/k-12/airplane/ngnsim.html but don't expect overly realistic answers. You have to use the Tunnel Test Mode for off-design performance after entering all the data you have available. And you should pick the "turbofan" engine type.