Is the original Heavy Rain tech demo in any way connected to the final game?  Because I think the prostitute from the demo quick look is the girl from the tech demo.  Am I wrong?

nothing and that demo with all the stuffed people is not in the game either

actually that demo with all the stuffed people and butcher guy comes with the special edition as a DLC off shoot chapter

looks different, but sounds the same. probably a wink and a nod sorta thing.
 
i doubt they're connected since the tech demo is a casting call for what seems like a cheating-husband killing role.

I believe that they actually said that it is the same person.

I don't know about they are the same person, but definitely the same model, or just based off of the same person.

Watching the QL I had the feeling I seen this before, as screenshots in an issue of EDGE. But it was just called "crying girl" or something like that.