1a Why do my constructors automatically build economy starbases on non economy resource points? For instance if I send a constructor to a military resource point it automatically builds economy/mining starbases.
Mining starbases are the only type of starbase you can build on a galactic resource. Due to this, the game automatically assumes, that you want to build one, when you send a constructor to a resource.
1b Should I be adding economy or military modules to fully utilize this resource?
You need to add mining modules, if you want to fully utilise the resources. Starbase defences, however, are entirely pointless. Even a handful of mid-game fleets will be able to destroy a fully outfitted starbase. You're better off defending them with a fleet.
2. What exactly are "full battles" in the options menu and how does a battle play out if I uncheck the automate full battles button?
"Full Battles" are referring to the Battle Viewer, which is a cinematic representation of the battle (usually between two fleets, but you can adjust this). If you disable it, then all battles are directly resolved on the map.
What I'm hoping for a method to manually control space battles so that fleet tactics can give me an edge in combat.
All battles are auto-resolved. There is no way to manually control them.
2a In the ship builder I select an existing design and press "Upgrade". This results in the shipyard showing me the hull/chassis but none of the weapons, modules, and defenses that I would expect. I would really like for those to be included so that I can easily see if my own design is more efficient without having to write down the existing ship's parts.
Go to the Interface-tab under Options and disable "Remove Functional Components When Upgrading A Ship Design".
2b How does "Focus" work on the shipyard? I believe that it automates the module priority on pre-configured ships but I'm unsure because it only lists the basic components.
"Focus" refers to the Auto-Design option. The Auto-Design automatically creates combat ships for you, using the Focus-setting as a guideline. However, the Auto-Design's ability to follow those guidelines depend on what weapons and defences you have researched. The results are sometimes weird and/or non-optimal, but for a starting player they are good enough.
Are there any must have mods that I should visit first?
If you are just starting out, then there are no must-have mods, in my opinion. Once you know the game a bit better, you might want to look into the fix-mods (MarvinKosh's Space Weapons Fix Mod, Tolmekian's TechTree Fix, Autumn Twilight, and APT 1 and 2), but they aren't mandatory. It's entirely possible to play the game for years, without noticing any of the bugs they fix.