I understand that part but: 

1) originally we were also able to mine asteroids for more income...

Furthermore,

2) What technology do you need to place these modules on on the starships, because I have capped technology and the feature is still not available

I would also like to add that these starbase modules are not the same as they were in GalCiv 2. In GalCiv 2, mining starbase modules were unlocked by factory techs. In GalCiv 3, they currently have their own techs.

So yeah, you're wrong about everything. Starbases are fully implemented and have modules and everything. Economy Starbases are particularly useful.

Have you tried sending more constructors to your starbases to add modules? Because they are most certainly in the game.

The only useless types of starbases, for now, are the influence and mining bases (only if you don't use/need the resource).

The economy and military bases are quite useful.  Military bases are a good way to establish a beach head of sorts when beginning an offensive and holding off the hordes of fleet the NPCs get to build due to their difficulty bonus.

I just purchased Galciv 3 on steam, and couldn't believe that mining asteroids fields wasn't in-game and was only being "considered".

I'm a long-time Galciv 1 & 2 player, probably put in hundreds of hours of gameplay. If this option isn't put into the game, Why have asteroid fields in the game at all?

Merely as an obstacle to pilot around? Silly. Eye candy? Silly.

Yeah, I think they work

Asteroid mining is in game, it has just changed since GCII. Now asteroid fields are where you find and mine Derantium.

The culture star bases don't seem to have the power that they did in GCII. They work, but the effect is very weak. Most of influence seems to come from planetary influence created by your culture buildings and culture research. I am not certain it is even worth building anything but econ star bases. On the other hand, it has occurred to me that since the econ bases power up the planet so well, the culture bases might also work better built within range of one of your own planets as a multiplier of the culture that seems to emanate from the planets. I'm not saying the remote bases don't expand your influence. It is the improvements that don't seem to help much. This is just my impression. I could be dead wrong.  

I thought the relic mining was working in beta 2 but they are not working now, that I can tell. I just won an influence V on a huge map vs godlike AI, (about 350 turns), I had the Altarians as an ally. I was too chicken to go it alone at godlike. All of the AI did pretty good. The Yor starts slow but came on strong by the late middle game. Frankly, I pretty much traded my way to victory. The AI is always broke and will trade anything but their planets for cash. The Yor agreed to sell me a planet but they wanted all my credits when I had about 15,000. I was able to stay ahead in tech and if they started to get too powerful I would buy 2-3 of their best ships for a few tech and a bit of cash.

Another AI problem, I was playing with uncommon habitable planets (not rare but the next one up). There were only about 30-40 habitable planets on the huge map and the AI seemed to give up on colonizing pretty soon. I wound up with 15-16 planets and the AI had only their home planets and 1-2 more.

Regarding the asteroid mining in GCII. The first thing I did was upgrade my mining ship for a colony ship and I never built another. It might be just me, but the return on asteroid mining just didn't seem worth the effort vs the other resources available. I don't recall what the mining pay back was but in my memory it was puny compared to trade routes and putting star bases on top of anomalies, (or whatever they were called) . If I am wrong, tell me what I was missing.

The way I see it, you do mine the asteroids. The only difference is they tell you what you are mining and where it is in the asteroid belt.

Mine them too!  Well, collect gasses from them, we'd probably still just call it mining though.  Give a range bonus for mining nebula and manufacturing bonus for asteroids.  Or come up with another use for nebulas, but for nebula and asteroids to only have purpose to house exploitable resources is lame and putting them in for "terrain" in space is about as lame.  Anyone paying attention is not going to fight in them and autopathing avoids them that's not much for being "terrain". The map is 2d so your ships when around them in the z axis should be reasonable too.