Can I install a Postgresql 64bit on Windows and make connection to this db using Qt plugin which is 32 bit? If I'm using mingw(32bit) on Windows then I have to install Postgresql 32bit too?
You need the 32 bit libraries to link against Qt and your application. If you connect via Network (eg via IP 127.0.0.1) there shouldn't be any problems. I'm not sure for local sockets, but I would expect those to work too. Just make sure that you load the correct versions of the DLLs.