Ok I'm a long time galciv3 fan so much of the new game is familiar.
First, I thought I had selected the Terran alliance as my player. Turns out I ended up being a random player and I was playing as the yor. What the hell?
Second, remember how in 3 when you didn't want to build any ships you could highlight that button and said don't notify when the queue is empty or something like that? I don't see that here. I have to keep building ships forever?
Third, how do you mine the special elements? Durantium for example.
First try a restart on the game see if Terrains show up.
Second you cannot stop construction of something on the shipyard, you can however repeat build treasure ships research ships or when you get the proper tech modules forever, you can click on one of these you have building and this option will come up.

Third for resources build a mining starbase near one just like in 3. Have to research starbase tech first. If you are talking about one that is on a planet click the hex and a build option will appear.
Also only one core planet can support a shipyard. You can colonize nearby planets and not assign a Governor to it. This will cause it to give its stats to the core and through it to the shipyard.