As a matter of fact, double-clicking the connection file in the Navigator pane always opens details about the connection as a text, this is a correct behavior. If you want to get to the "Edit DB Connection" screen, you should double-click the connection in an Outline pane (below the Navigator pane).
Nevertheless, the main issue is related to the jobflow files, right? I can see on your screenshot that the JBF files have incorrect icons in the Navigator pane. Could you also please tell me what happens if you double-click the JBF file? In case it opens the JBF file as a text as well, please take a look at the bottom of the main screen and look for an option to switch from "Source" tab to "Jobflow" tab. Can you see the tabs there? Does it work?
Can you also let me know how did you installed your Designer? Did you install the Designer as a new program or did you install it as a plugin to your Eclipse? Have you been experiencing the issue from the very beginning? If not, did you change anything recently?
Anyway, first of all, my recommendation is to install the Designer again from a scratch. Preferably you should install it as a new program (to a new location), not as a plugin to Eclipse. Please give it a try and let me know if it helped. If not, any additional information is highly appreciated. Thank you.