I just never have put in the effort to make use of all the features the game has. Maybe I'm just lazy. I am trying to make use of more of the features, but I still don't put that much effort into it.
Answers to your questions
1. I don't use them too early because I'm never sure what to use them on. As the game progresses, I sometimes do use them. Other times I never get around to it.
2. This is one of the features I've never bothered to investigate. I have no other reason.
3. I designed a lot of ships in GalCiv3 to make up for what I considered to be weak designs provided by the game. I've always felt the designs in GalCiv4 were good enough for me, so I've rarely designed my own ships. I didn't realize so many slots weren't being used, causing me to be using ships weaker than I could design. I'll definitely have to pay more attention to this.
There is one problem. I'm using a mod that "fixes" some problems with ship designs for the Onxy Hive so they will quit using ship parts that "allow" ship repair. They aren't supposed to be able to use repair, so the parts are useless most of the time. What's worse is that some of the parts actually do repair, which goes against the idea of the Promethion Born ability they have. Maybe the mod is causing some of that. I'll try to remember to check that the next game I play, when I will play as some other race and without the mod.
4. I actually have a military base above the bottom-center path. I put it there because the Arcean were sending so many ships that were finishing their turns near that area. I was too busy building ships and trying to destroy all of theirs that I didn't get around to building more.
The Arcean have quit the game. I'm sure some of it was due to my military efforts and some was due to my paying some other races to go to war with them. I started the game with 20 total players. I think there are only 13 now.
I have no problem with your questions. I know everybody has a different way of playing, and GalCiv4 provides many different choices. I've been trying the Galactic Challenges in this game to see if I can do better in the Prestige Victory area. I was inspired by this post.
I especially appreciate question 3. I think that may allow me to become much more powerful in future games.