Ok i'm not ENTIRELY sure what the issue is, but we'll go with this:
Your shipyards have no class asigned. Instead of looking down in the refit section, where its blank, look up top:
Task type: no activity.
Set it to: retool shipard for selected class, select the class. It will instantly retool because its the first design, and then you'll instantly be able to begin construction down below.
A yard can be retooled, for a nontrivial cost and time.
note: "the shipyard complex activity" section is in that window you linked.
The top third is the list of yards. middle is "shipyard complex activity". bottom is "create shipyard task"
The wiki could stand a substantial rewrite. But I for one am working on my graduate thesis, and don't have time to do anything
. However, once thats done, i may have time to get in there and do it-- as you figure stuff out, consider it as well!