statically linked executable

[yop]

so which of the dll's do i have to redistribute with my app?

In most cases you'll need QtCore4.dll QtGui4.dll and your compiler's dll (mingwm10.dll for you know which compiler) but in order to get a definite answer you should see which modules you use in your app and include the neccessary dlls (eg if you're using xml you'll need QtXml4.dll if you're using OpenGl you'll need QtOpenGL4.dll etc).

where should they be placed?

In your program's working dir, or in [WINDIR]/system32 with the later being a very bad choice leading to dll hell most of the times.

and is it possible, to link them statically, so that i needn't to have the dll's with the app?

yes