I would recommend taking some time to work through the examples and demos which come with QT. There are a lot of them, and they cover all of the tasks you mentioned.
The QT documentation is second to none in my opinion. I would take a look at the following classes: QThread, QFile, QTextStream, QVariant (if you want to save numbers to a file using a human-readable string, this class will help you with the conversion to C integer or float types).
Also, do try to understand the signal/slot mechanism. This is thread safe, so you can pass data between thread using this mechanism without worrying about all that stuff.