I'm assuming you know this doesn't really hide the file location - anyone could find it in your source code.
Yes, you can close windows from parents (or indeed from anywhere) but you need to set up your pop-up windows properly to do this - i.e. with names). Better to call a function from your onclick and open the window from there, giving it a name. Then, via that name, you can close it, write to it, reposition it, whatever. Look up any pop-up window script online and you'll see this - the name is one of the arguments you pass to window.open().
I'd be inclined to do what you're doing with a hidden iframe - saves the ugliness of an appearing then disappearing pop-up.
Just have an iframe with display:none set then literally just point your link at it (in the target="" attribute). Then the download prompt will come up (depending on the filetype of the downloaded file) and look as though it came straight from the main page.
What I'm experiencing is that the file downloads on page load, which I don't want. (I want the user to have to click the link.