Welcome to the forum! And, thanks for the kudos, glad you are enjoying the game.
1. To this one, bringing in cleaners is definitely helpful -- and they are cheap. But I would suggest trying to kill the command station sooner than you normally would, if you think you can take on the entire system at once. That way you fight all of their ships away from their turrets, and then you can just go and clear off their turrets the one time without having to worry about them rebuilding. The downside is that if the planet is too strong, you might lose that battle... and then the game, as the freed AI ships then flood over to your planets. But if you are strong on defense, and/or have a big enough fleet on their planet, you can save time and work by killing the command station earlier than is generally otherwise recommended.
2. Sure, just open up the stats menu (click the scores box) and then see the Expenses by Player tab. It shows you exactly what is costing you resources, and where.
3. Well, that is a bit of a vague question, I am not sure if you mean strategically or just how to functionally make it work. It has a variety of build templates in there that make its "nodes" filled to start. Or you can start empty, I believe, and fill the nodes as you want. When you select it, it lets you select the things you want on it. If you meant strategically, generally that one is for use against swarms of smaller ships -- but since you can customize that ship's loadout, you can alter that to some degree.
Hope that helps!