2. I struggle with efficiently organizing my fleets. I don't understand what the "pin" option does or how to use it. My fleets generally end up messy and jumbled and it really takes me a long time to organize them the way I feel they're most effective.
Don't forgot control groups and hotkeys. I usually like to keep each individual capital ship in its own control group (honestly I usually only have 1 for most the game, the Akkan); I also put specialty groups, like siege frigates, into their own control groups as well.
I also like having ship-producing planets set to their own control group (usually 0 or 9) ... so, if I notice that I have the credits for an LRM, making the ship is as easy as hitting 0 (select planet), A (enter frigate menu), E (queue up one LRM), which takes me less than a second. Compare that with zooming out, searching for the planet you want, clicking it, then selecting the menu and ship. Seems minor, but it's a huge time saver in the long run to develop this kind of habit. This also helps you continue building ships while focusing on other things, like battles.
Also, remember that Alt-clicking a unit in a gravity well will select every unit of that type.
Also also, you don't have to click on enemies on the screen to have your units target them - you can also issue an attack order to enemy units displayed in your empire tree on the left. This makes it much easier to target specific units (like, for example, if someone has a swarm of illuminators and a few subjugators, you can use the empire tree to easily target the subjugators). This helps to avoid the 'needle in a haystack' problem when fleets become very large.
6. What upgrades are most essential and should be gotten right away?
In my opinion, I think TEC should initially focus on Civic-tree upgrades. The first two upgrades I get are the ones that make producing structures cheaper. In total, you'll spend 900 credits, 75 crystal getting these two upgrades. However, metal/crystal extractors go down in price from 250 to 150, and you'll have these upgrades done before you leave your first asteroid. If you conquer, say, 4 more planets (for a total of 6), each with 3 extractors each (just an average), you save 1,200 credits. Additionally, you save money on producing frigate factories. (450 down to 350). Afterwards, I usually focus on the mining upgrades (crystal and metal) and then the colonizing research, if and when I need it as it comes up.
When you capture planets, make sure to upgrade their civilian infrastructure to maximum as soon as possible. This is easiest for asteroids, which have just 1 upgrade, volcanics have 2, arctics 3, deserts 3 and terrans 4. If you do not upgrade, you will actually lose a lot of tax income (the amount is staggering ... I used to neglect these upgrades, then was horrified to see that I'd lost around 80,000 credits to underdevelopment by the time a 2-hour game was over)
8. Here's a major problem for me... How much time should I spend fortifying a planet before I move on to take over the next planet? I seem to either over-defend my planets, or I'm too aggressive in taking new planets and end up getting attacked at another planet while on the move and everything falls apart.
To quote General Patton, 'a fortress is a testament to the stupidity of man.' In general, it is better to take the resources that you would spend on turrets and instead just make more ships, because these are mobile, while turrets are stationary.
This doesn't mean that turrets and other structures don't play their part, though. All too often, players will leave a planet completely undefended - a good player will take advantage of this, and fly in a couple of siege frigates to eliminate a planet's population (and thus bring its tax income down to 0) without opposition. Only takes 2 frigates to do it, and many times you can retreat the frigates before help arrives. So, in such cases, having 1 or 2 gauss turrets around the perimeter as a safety precaution may be worth it.
However, your best defense is proper intel. Know where your enemy is, know what he's doing, and you'll be able to predict his actions more accurately. Having scouts drop remote sensors on planets (civic tree upgrade) is invaluable, because you will be able to see what planets he's fortifying, what planets he's not fortifying, and where his fleet is. If you can't drop a sensor (say, on magnetic clouds, for example), just leave a scout frigate there.
Anyway, TEC units are relatively weaker when compared to the other races, so I think TEC's best strength is to build a stronger economy and out-produce the enemy.