My application crashes

[spirit]

Next thing is, I do not think it is necessary in the

void MainWindow::slotExecute()

void MainWindow::slotExecute()

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to check if the sender is NULL, because if there is no sender, this SLOT won't be called, right?

you can call this slot by yourself somwhere in your code, so this check is needed.
note:

...Slots are normal C++ functions and can be called normally; their only special feature is that signals can be connected to them.