I'm new with Platinum.
I find this problem: no matter if i use external Midikeyboard or the virtual keybord e.g. in Rapture there is always a very long latency of about half a second until I hear the Sound. this makes it absolutely impossible to record.
 
I also only hear the sound when the "input echo" is switched in, is this correct?
Is there anything I can assign on memory (have 16 GB) to Platinum or where could be a wrong Setting in my system?

Yes, Input Echo is necessary to monitor what you're playing.
 
In order to get the latency down low enough for real-time recording, you'll need to reduce the audio buffer size. If you're using ASIO, that will be set using your audio interface's control panel; for other driver models, SONAR sets it. Press "P" for preferences, scroll down to Driver Settings and look for the Buffer Size slider. If you're using ASIO, it'll be disabled so click the button labeled "ASIO Panel". If you're not using ASIO, you can simply move the slider to the left to lower latency.
 
As a general rule of thumb, 5ms or less will be fine for real-time soft synth playing. If that's too low (the lower you go the more stress is placed on your CPU) then as high as 10-20ms may be OK, depending on how percussive the patch is.

Wilkommen.
What is your sound card or audio interface?

MIDI delay is often caused by CPU intensive plug ins. By pass any look ahead plug ins. 
ASIO audio interface is highly recommended for recording to get output latency down.