I want to make a popup type of layer on the iPhone 4. Is that possible? Like in this screenshot:
On the iPad, you can use the built in UIPopoverController to achieve a very similar control. There is no built in control that shows like a popover in the iPhone. You will either have to create your own or use a different control.
There is an open source Popover for iPhone. I've never used it but I think it will fulfil your needs: https://github.com/werner77/WEPopover