I didn't totally understand your question, but I'll try to answer it anyway:
1. If you only want the picture to show while the user is clicking on the link, you can convert the link to a button, edit the button (by double-clicking on it), and then embed the picture in the down state of the button.
2. There's no way to create a pop-up window in the current version of Catalyst. However, you can write code to do this using the PopUpManager in Flash Builder.
Expanding on this... you could make it so that clicking the link displays an image over top of other parts of the UI, and the image can have a "close" button or other means of hiding it (such as clicking the link a second time). The only things you cannot do in Catalyst are have the image stick out of the bounds of your app entirely (overlapping other applications running on the OS), and have the image's location be draggable like an OS window.
If you're ok with those limitations, here's how to do it in Catalyst:
(these steps are written in a little bit in shorthand, so let me know if you're not sure what I mean anywhere)
1. Import your image into Catalyst and place it next to the Button you're using as a clickable link (not inside the Button)
2. Convert the image to a Custom Component. Name it something like "ImagePopup."
3. Duplicate state, name the first state "closed" and the second state "open"
4. In the first state, hide the image
5. Go back to the link/Button and add an interaction: On Click > Play Transition to State > ImagePopup: open
Now you have a way for clicking the button to show the image. You can position the ImagePopup component so that it overlaps other parts of your UI, just like a floating window. Next you can add an "[x]" or "close" Button inside the popup that closes it by transitioning back to the "closed" state.
Hope that helps!