- Executing MiniDumpWriteDump within the specific process provides healthy dump file. 
- Executing MiniDumpWriteDump from external process, where hProcess and processId point to the mentioned specific process, provides a zero length dump file 
- Same as #2 just pointing to FireFox for example provides healthy dump file 
The specific process I am trying to dump is running with low privilege as far as I know, and my external process is being executed from Administrator CMD window.
[DllImport("dbghelp.dll",
            EntryPoint = "MiniDumpWriteDump",
            CallingConvention = CallingConvention.Winapi,
            CharSet = CharSet.Unicode,
            ExactSpelling = true,
            SetLastError = true)]
        private static extern bool MiniDumpWriteDump(IntPtr hProcess,
            uint processId,
            SafeHandle hFile,
            uint dumpType,
            IntPtr expParam,
            IntPtr userStreamParam,
            IntPtr callbackParam);
Notes:
- I am flushing, closing and disposing correctly the file stream
- MiniDumpWriteDump return false and GetLastWin32Error returns : -2147024597
- The mentioned specific process (a dot net server project) has the same Security options as FireFox (the dump works on Notepad++ process for example).
 
                        
Ok.. found the solution for that..
The external process project was build for "AnyCPU" platform (and as it doesn't execute only-64 bit commands, it was running for 32-bit). Setting it to x64 made it possible to dump another 64 bit process.
And I would recommend to anyone who encounter this issue, to create separated projects, one for 32 bit and one for 64 bit.