The purpose of the forum is to support Qt Newbies. The is no service level agreement that requires answers from volunteers within minutes, hours, or even at all.

Qt is a cross-platform library not a compiler. If you can build C++ code for your engine/game that uses all those libraries and components without the Qt library then you can almost certainly build the same program including the Qt library for some components. You will need to use a consistent C++ compiler toolchain across the project's C++ components, including Qt. There also some documented collisions (and workaround) between Qt and Boost Signals if they are also present somewhere it that pile of pieces.

If you want to use DirectX directly in a program that is also using the Qt library nothing is stopping you (in some configurations Qt5 uses a DirectX abstraction layer (ANGLE) itself). Of course you will have to develop for Windows only and you will likely have to use Microsoft's SDK and compilers (possibly counter to your "Platform: 2. Others later on" goal). Ogre3d abstracts some of that away but requires Microsoft's tool chain on Windows AFAICT.