Why is pa-db.com such a useful site? There we can learn a lot. For example a bit of browsing teaches us that an energy plant has a cost of 450 metal but no specified cost in energy. While trying to learn how much energy it would cost to build one we find that a Commander (CMD) builds with a energy consumption of 1500 / s and a metal cost of 30 / s. We can also learn CMD builds one in 15 seconds. Poking about more we find that if we wanted to build an energy plant as fast as the CMD builds one, but using regular Fabrication Bots instead, we have to use 3 of them. Look at how much Energy they's spend and compare it to the CMD. That's right. 3000 Energy / second for 15 seconds versus the CMD's 1500 Energy / second. How do I use this information in my game? At the early part of the game, where resources still are very sparse, make sure to have your Commander building Energy Plants. Let your Fabrication Units (FUs) build Metal Extractors, Radar and Factories. The faster and cheaper energy will help your economy grow at a faster rate. And good economy allows for plenty of guns, rockets and all other things that go boom! Disclaimer; All info in this post is about the most recent builds and is, like the rest of the game, subject to change as it is still being developed. Internet high fives to everyone at Uber Entertainment for doing a great job!
A lone commander cannot build energy fast enough. Normally you need to get some other fabricators assisting the commander. That's generally everyone's opening build. 3-4 metal extractors > 1-2 energy plants > bot factory > crap ton of energy plants
Yes the commander is more power-efficient at building so you should use him to build non-stop unless you are using him aggressively early game.
Your analysis is a bit misleading and sort of wrong. Building energy with your commander is good but not for the reasons you state. Say you have your commander constantly making power plants and 3 constructors constantly making factories. The drain of this whole system is 4500e/s and the both the factories and the power plants are built at 30m/s. This is identical to using your commander to make the factories and setting the 3 constructors to make power plants. In both cases the structures are produced at the same rate and with the same drain on your economy. Sure in a sense the first case the power plants cost less energy but this is offset by the factory costing less energy in the second case. It's not just that power generators cost half energy when the commander builds them. Everything costs half the energy when the commander builds them. Based on this it doesn't matter whether your commander is building factories, mexes or power plants. Whenever your commander is constructing you are 'saving' energy. I think that your heuristic "build energy with the commander" happens to be correct but for the wrong reasons. I think I have a better heuristic, "maximize the amount of metal your commander spends". To spend 1 metal with your commander you need 50 energy but to spend 1 metal with a constructor you need 100 energy. Spending more with your commander instead of other constructors saves you energy. This means that walking between construction sites is wasting energy so expanding with your commander will lead to poor economic growth. You should not make too many factories in the early game and the only major task remaining is to create power generators. So it is often a good idea to leave your commander in your base making power generators.
While your advice is very good too, I'd like to point out that i am talking specifically about the early part of the game. Here you want as much Energy as you can get (assisting the Commander is not a bad choice either, if eco allows for it) while you might make decisions on how much resources you want to spend on building Factories or Metal Extractors. For my part, it is not unusual that I send little pairs of FUs out on MEX duty, and whenever my economy allows i'll just grab the ones closest to my enemy and build factories. No matter that decision, i probably still want my CMD building Energy. Later on, it'll probably get involved in building Advanced Factory and from then on it's more of an open field what CMD might do because you want to keep it out of harms way as well.
In the early part of the game there is no problem with producing factories with your commander (as long as you actually need the factory). I see your point though, when deciding what to do it is usually easiest to let your commander spam energy while building factories with constructors. This ensures that the commander has as little downtime as possible so you save as much energy as you can. To save energy you should frequently toggle pause on constructors such that your metal storage hovers just above empty but you never stall. Also make sure that your commander is working as often as possible. This will let you build less energy so you can expand your metal production faster and so expand your energy faster as well.