So I'm not 100% sure, but with my 2 play throughs (one as Techno Union and one as Trade Federation) I believe you are suppose to buy those through the global market. As Techno union you can build almost every droid/tank but have limited naval options. Trade Federation was opposite. I could literally only build droidikas but had more options to ship designs. In both games, I had to rely on the global market to buy the things I couldnt build myself. Again, I'm not part of the mod team so I'm not sure if this is what they intended or this is a bug they need addressed.

I think you are right, but for the main faction with Dooku I think he should be able to produce them as well. At least later, because the Techno Union works under his rule, so why should he pay for the droids and the tanks.
At least a licens production should be able for him, but if you try to get one, they want more than 600 civ. factories to get it done for just one license?? Its pretty obvious that the devs blocked the licenses that way...

as you go through the CIS focus tree there are production licenses you pick up along the way. however, the market is the main source of equipment for both sides. Corporations only produce limited options, but can also produce those locally. In my play through as the CIS I have over 100k B1s well before the war, I kept buying them. But the market does not stockpile much so you need to keep going back every few days and buying more of everything.

Like base HOI, everything is done through the focus tree, and most major players respond to each other. So if you play trade fed and never blockaded naboo, you can stop the entire progression of the republic player. As the republic the war only really starts with the battle of genosis, so both parties can control when teh war starts through their focus trees.

After the CIS moves to the war focus tree there are more licenses available, and tech up also helps widen the pool of possibilities. But besides basic B1 production, I focus on civ factories and growing income to keep buying.

had (have?) a more weird problem .. when i start all my production is at 0% effectivity and stays there untill i research dispersed industry with the minimum 5% effectivity .. THEN i can start building items and effectivity grows ..