First, as soon as you research "space weapons" you can construct Star Fury and if you have "space weapons" and "interstellar construction" you can build defenders.

What i think the problem is that you are researching a tech, and the tech definition says you will unlock that ship, but it also says what others techs you need to use it, so i think you should research those techs or just make a new ship.

When you say that even when you make a ship from a template you can build it, this sounds as one of the bugs that was fixed in the 1.96 patch, i remember reading the change log and seeing a bug very similar and it was fixed so try updating (And as the mods always say,dont overwrite ship designs).

Try this, When you ake a ship use a template, then save it with a new name(without any weapons or anything just a test so you could see if the problem is with the weapons), if that works then go to the research scrren and find a weapon tech you are sure you ahve and look for the weapon that tech gives adn try putting it on an upgraded design of the first and saving it with a new name, maybe that will work, if not you have find yourself a new bug.

Miniaturization is usually the culprit