Assuming this refers to TARGET2-Securities, the European securities settlement engine, I don't know of anything relevant in Qt except possibly the Qt Purchasing API which supports In-App Purchases, but could potentially support other financial features in the future.
In the context of the QString class, the += operator is overloaded to perform string concatenation. Several other classes also overload this operator. See the Qt documentation under operator+= for details.
We covered this in a previous webinar which you can view on demand. See https://www.ics.com/webinars/qt-test-framework There is also a follow-up webinar available on "Qt Test Driven Development using Google Test and Google Mock" that you may find relevant.
I don't have direct experience with it, but my impression is that it is less mature than the Android version, but people have successfully developed iOS applications and had them accepted in the Apple store. You may need the commercial version of Qt in order to meet Apple's requirements for applications in its store.
With the "traditional" connect format (the first example on slide 56) Qt does not check that the signals and slots are valid at compile time. The other three examples do provide checking at compile time.
Hard to say - it depends on the look and feel of your application. You may find that you need different user interfaces on each platform. If your desktop is Windows 10, possibly with a touchscreen, Qt Quick may be a good fit for both platforms.
I have not used Scilab, but we have used similar tools like MATLAB and integrated it into a Qt application. I'd need to understand more about Scilab and how you were using it to evaluate how hard it would be to do this.
The original Qt Quick controls are aimed at desktop use, to run on the desktop platforms and replace widgets. The new Qt Quick Controls 2 or Qt Labs controls are lighter weight and better suited for use on embedded platforms.
You can if the compiler is supported on that machine and platform. In many cases that is not true. You can use virtual machines running on the same hardware with different operating systems to allow you to build for Linux, Windows, Mac, etc. Tools like Jenkins can be useful for automating builds for multiple platforms.
It is hard to give a short answer. I think Qt is healthy and has a bright future. It will probably follow industry trends, as it has when mobile devices became popular, and more recently embedded systems with touchscreens and powerful CPUs and GPUs. As new technologies become popular, Qt will likely add support for them (support for speech recognition and generation is coming in Qt 5.7, for example). It looks like Qt will also expand into lower level functions, as evidenced by the recent support added for Modbus, CAN bus, and Bluetooth Low Energy.
There has been some discussion of this, and there is an interesting fork of Qt called CopperSpice that replaces MOC. I think this is unlikely to happen, certainly not before Qt 6, because it would probably break binary compatibility. I do expect to see some features of Qt to be deprecated because C++ provides equivalent features. This has happened for algorithms for containers and could happen for threading, for example. The foreach keyword I mentioned for iterating over containers can now be done with a for loop in C++11.
I'm not familiar with any on-line courses that I can recommend. Reading the Qt documentation and tutorials and doing hands-on programming would be my recommendation. If you can find an experienced person to mentor you, that can help when you run into problems (or make use of the Qt forums and mailing lists).
Some of the common back ends on Linux and embedded platforms are OpenGL/ES, the Linux frame buffer, Wayland, and xcb (X11). To use QML you need support for OpenGL, so the most commonly used back end on embedded platforms is OpenGL/ES (the eglfs back end). DirectFB is another option but its future is uncertain as no one seems to be maintaining it (not the Qt back end, but DirectFB itself).
Each Qt module has a version number and they don't always match the Qt release version number. QtQuick 2.6 does correspond to the latest version in Qt 5.6. Right now it is just a number that is increment each time the module has API changes, but won't necessarily change with each Qt release. There has been some discussion about making the versions the same as the Qt version number.
The only other Qt IDE I have used under Linux is KDevelop. I have used Eclipse in the past but I don't believe it supports Qt anymore. There are some others, but I don't have personal experience with them.