You need to put a constructor ship inside to build any upgrades. As for the research, there used to be a hot-key to force an end to the turn (shift-click or similar on the turn button).

You're welcome for the tip, and thank you for the info about the research, I just hit the same problem!

In this current alpha iteration if you send constructors to your starbases before the tech is available they seem to station themselves "outside" so you have to eject and then move into the starbase again. Once you do this the tech modules materialize once you click manage and look on the right hand side - you then select the initial tech module and add which then brings up other related techs you can also add (if you have researched them of course - which you did ).