Emperor Belos custom cursor

You are considering creating an educational guide on how to create a program in C# that uses asynchronous data loading with .NET Interoperability Services (NuGet) library, including error handling. Your task is to develop a function which takes in input a list of user-defined tasks and executes these tasks concurrently using the "asynchores" package for managing background operations. The program should handle errors during execution, log them into a file named `error_log.txt`, and retrying after an error occurs. In addition to this, you have been asked to add unit tests with at least 5 test cases: one where everything works fine, two where the network is down, three where there are invalid data types in the list of tasks, four when all operations fail, and five involving a new task `Task B` that might throw an exception. Also implement caching mechanism for retrying failed tasks.