Ship designs - I enjoy designing ships as much as I enjoy playing the game, but that doesn't mean you are missing anything if the stock designs are working for you. Forgetting about the idea of building a neat looking ship, I find that I need to build ships that are cheaper, have better range, or different fire power than what the game designs allow. For instance, the starting colonizer has good range and okay speed but it takes a lot of turns to build early in the game. I can design a ship for a lot fewer turns to build if I leave off some life support and engines to colonize a nearby planet.

I occasionally watch a battle if it is going to be close or if there are enough ships to make it interesting. You can learn some things about your weapon choices from the stats at the end of the battle. I skip most of them.

I play a lot zoomed out as well. I have to zoom in sometimes but I can't seem to get the hang of playing close enough to see ships instead of icons.

The stock designs are appalling, but then again the AI uses them too so really you're just giving your self a level playing field. Watching battles takes too long, and the results are often incorrect anyway (you can regularly watch your ships vanquish the enemy in the field, and then return to the main map and find they've actually all been destroyed).  Zooming all the way out can make it a little harder to play in tight tactical situations, but does no real harm beyond that. 

1.  Ship design is pretty much mandatory, especially on the higher levels.  You can specialize a ship to a particular purpose and become so much more efficient.  Why build a long range colony ship when your target planet is within your borders?  Maybe add an engine to speed it up instead.  That sort of thing.

2.  I'd say to watch a few battles until you see how different ships and weapons perform.  Then you can just build missile ships and carriers.  Watching them further is a waste of time IMO.

3.  I zoomed in to see the pretty graphics a few times, but you can miss what's actually going on in the game if you stay zoomed in.  The icon level has a lot more utility than the graphics level.  That is, when the icons work right.

Same here. I use the strategic view only for navigation and, well, for strategy. For everything else the map is zoomed to whatever level makes most sense but always below the level where the objects turn into icons. It just looks better that way and is more immersive.

I usually watch the battle movie, too. It gives a certain satisfaction. Plus, you do get info on how the weapon-defense setup is working. Although, mainly it's just for the enjoyment factor.

Others have commented on how using the Designer can give you an advantage.  Me, I also like designing ships because I find it relaxing. My day job isn't very creative.  I often enjoy spending hours designing ships (not even playing the game) because it allows me to be creative.  I also (try) to write Sci Fi and I can design ships in the Designer that allow me to visualize the ships in my stories.  In the Steam Workshop, my Banshee Class Cruiser is actually a design from one of my stories.  It was fun to "bring it to life."

I occasionally watch battles just to see my designs fight and to get stats.  However, I mostly don't watch.  It's unrealistic (why would my long range missile ships move closer to the enemy?) and since I can't change the outcome, it wastes too much time.

Like others, I use the map zoomed out to navigate and for planning, but zoom in closer for "tactical" movement.

To each their own.

Modder who designs ship sets shocks forum by declaring support for ship designer