In case of use Qt for Windows development the problem of the icon showed as window system icon is automatically resolved by add the .ico file as Windows resource. Windows already allow such feature and no need of additional efforts. In case of same code ported and compiled under Linux or Mac this step is not automatic. However, basically, what you need is to simply manually assign by code your icon to the window. If you are moving from Windows application project add your .ico file to the Qt resource file (.qrc) of your project and, once done, add this line in window initialization phase:

QApplication::setWindowIcon(QIcon(":/my_prefix_if_any/my_window_icon.ico"));
If you want to create a QPixamp object with transparent background you simply need to fill the entire area with transparent color immediately after created. After doing this you can start to draw over.

QPixmap MyPixmap(QSize(32,32));

MyPixmap.fill(Qt::transparent);

// Now you can draw into
// .......

If you want to know how to draw into a QPixmap check this post.
Draw inside QPixmap can be made using QPainter object. Basically you have to pass to QPainter the pointer to your QPixmap (already created with fixed size) and you can draw inside as the same of window area painting.

QPixmap MyPixamp(QSize(32,32));
QPainter Painter;

Painter.begin(&MyPixamp);
// Here paint inside QPixmap
Painter.setPen(QPen(QBrush(Qt::red), 1, Qt::DashLine));
Painter.drawRect(0,0,32,32);
// ...
Painter.end();
Eclipse is the "official" IDE proposed by Google for Android development. Usually Android app are written using Java code but for some specific task could be necessary to use native C/C++ code to interface with the Java side. Here a tutorial about how to configure Eclipse for a mixed Java and C/C++ code and how to develop it.

Java language used in Android allow to communicate to external libraries written in C language through JNI interface. However is possible to use only dynamics libraries and there is no possibility, for obvious reasons, to use static libraries instead. In case you have a precompiled static library you need to use in your Android app you can create a dynamics as "wrapper" for your static library.