How do I use dictation paste with applescript?
If dictation is enabled and running on your system,  the command you would say to paste something from your clipboard is “Paste That”.

If dictation is enabled and running on your system, you can say the command “Show Commands” … which should open a window showing all of your dictation commands


  Also, is there any command for cursor placement after paste?


Look at the "Navigation" section of the image below for cursor placement commands



Once this window was open you can then say something like. “How Do I Paste”.  This should narrow down the results to all of the dictation commands with the word “Paste”