Never build Kols. They're completely atrocious and offer nothing useful to a fleet for their costs. Otherwise, you need many more Hoshiko Robotics Cruisers. I'd say about at least 25% of any TEC fleet should be Hoshis. LRMs and Gardas are also essential for dealing damage and killing off SC/LRF quickly.

Capital-wise, the Akkan is arguably the best colonizer capital as of the most recent patches, giving 1/2/3 free extractors and a 33%/66%/100% temporary bonus to extraction rates with its Colonize ability.

As it stands, carrier capitals are fairly powerful, each in their own respect. For the Sova, this means having 3 to 4 Missile Platforms out at the same time (which will help to bolster your fleet), or denying your enemy of the credits of one of their planets.

I wouldn't go so far as to say "never".  The Kol is a decent late game capital ship, though certainly it should be avoided in the early game.  You should at very least have a few antimatter regeneration technologies researched before you bring out the Kol. 

The Kol has been nicknamed by the fanbase as the "brick", because it's one of the toughest capital ships in the game but it really doesn't do a lot.  Its abilities cost exorbitant amounts of antimatter, but it actually has very poor antimatter capacity as far as capital ships go.  This means the Kol usually gets one or two uses of its main abilities before it's out of antimatter.  After that, it's a brick and doesn't really do that much.

Bring out the Javelis LRM a little earlier, don't stick with cobalts too long.  Unless your opponent is very heavy on the carriers, cobalts should never make up the majority of your fighting force.

As I said, your top priority (particularly as TEC) is to bring out at least two other unit types, preferably the Javelis LRM and the Hoshiko Robotics Cruiser.  If you can round that out with carriers or gardas, that simple selection of units could last you the entire game.

Akkan is always good, but you probably don't need more than one.  Sova is an excellent choice in the early game, but it fizzles out in the mid-game and is a mediocre choice in the late-game.  Kol is absolutely horrible in the early game, but it becomes respectable later on.  The Marza is a solid choice, though I wouldn't pick it as your first capital ship.  Dunov is something that is best reserved for later on.

Typically my opening run (now) goes like this:

- Build Akkan

- Build 2 civic labs, get Ice and Volcanic colonisation techs

- Research fleet capacity upgrade

- Build 20 cobalts

- Colonise a wealthy amount of planets

Where would building the Javelis frigates fit in?

Just another side question, I played a FFA Diplomacy and got lost. In the first 10 minutes, I was getting missions from the AI. What do I do? Continue colonising and expanding my empire or complete these missions?

Before researching your fleet capacity upgrade.  Perhaps I wasn't clear before: do not build 20 cobalts.  You can build 3 or 4 to help with colonization, but don't make them the backbone of your fleet.  The only time to build large numbers of cobalts is if your enemy is spamming carrier cruisers or flak frigates, which usually only happens online.  If you're ready to build a proper fleet of reasonable size, upgrade to Javelis right away and build 20-30 of those.

Secondly, don't wait for your fleet to start your colonization.  Send your capital ship out immediately to acquire planets.  Heck, you can even go so far as to send your capital ship in one direction and a few cobalts in the other direction to colonize planets quickly.  There are usually a few planets with low militia counts nearby that your frigates can handle without capital ship support.

Thirdly, your plan should always be based on what feedback you're getting from your scouts.  There is the off chance that you will begin in a position with few ice and volcanic planets, in which case you might seriously consider delaying civic labs altogether and going all-out military.  Even if there are a couple of ice or volcanic planets nearby, if they have high militia counts or are out of your way, you might just save them for later.  Similarly, if you encounter an enemy nearby (this happens very often on larger FFA games) you may want to go all-out military.

When learning the game, you may want to change the settings to "locked teams".  The AI's will not give you missions in this setting and will not be able to form alliances between each other.  This is just one less factor you need to worry about when you're still learning the ropes.

In general, you should never stop your expansion in the early game for any reason except to attack or defend.  In the long run, having a large empire pays off spectacularly.

I presume you're TEC.  The way you described it, you allowed the game to go on way too long.  The longer the game goes on, the harder it will be to win as TEC.  They're very much an early-hitter faction that depends on building a superior fleet and economy to overpower the enemy.  Once the tech tree is mostly done and the fleet cap has been reached, TEC has almost no advantages over Advent and Vasari.

The answer to huge swarms of strike craft are actually capital ships.  Each faction has one capital ship with a special ability that is custom-made to punish massed strike craft.  For TEC, this is the Kol with flak burst.  This ability will damage all strike craft in the area of effect.  Unfortunately, it takes 2-4 bursts to kill depending on the type of strike craft and the level of your Kol.  So you will need to complement that with other units.  Vasari and Advent have it easy; their special abilities actually shut down the bombers for a short period of time, whereas TEC are still taking the full brunt of that damage until the bombers are killed.

You'll need a large formation of gardas, and having your own carriers equipped with fighters is a good idea.  Two Kols with flak burst (preferably upgraded, though that might not be feasible) will be able to deal massive damage to the swarm of bombers making it easy for your other units to finish them off.  However, you will need to time these abilities perfectly so as to hit the maximum number of bombers with each burst.  If left on autocast, flak burst will be wasted on small groups and will be on cooldown while the main swarm is overhead.

Beyond this, damage dealers are the other side of the equation.  TEC is the lowest damage dealing faction in the late game, but the Javelis LRM and Kodiak Heavy Cruiser still pack a competitive punch.  Back them up with hoshikos to keep them alive and you can win battles of attrition quite nicely.  As TEC in the late game, however, you have to be aware that you're a faction of attrition.  You can't overpower a fleet of equal size and you'll need to win by being able to replace your casualties faster.  Be prepared to lost and replace capital ships, as well.

Getting high level capital ships is a high priority for TEC.   TEC capital ships are fairly weak in the late game, having few fleet support abilities.  However, if they can reach level 6 this changes and they become very powerful.  The Marza and Akkan in particular have awesome abilities when they reach the highest levels, and the Dunov and Kol have great level 6 abilities as well.

Very much so.  You should definitely focus on your special abilities.  The unit AI is smart enough to focus fire, so for the most part you can leave combat frigates to their own devices.  The only units you might want to "dance" around with are fighters and bombers, which have the mobility to actually move around enemies.

Yup, Advent vs TEC in the late game is positively a slaughter, and there's very little the TEC can do about it unless they have superior numbers.  Against the AI you could definitely pull it off (though you'd need a bit more experience as a player than you have now).  Against a human player, you can just forget about it.

Wouldn't call the Advent carriers "small", they're actually the largest and most expensive non-capital ship unit in the game.  They pay for all those extra squads, rest assured.  Strike craft is one of the few areas Advent actually doesn't have a substantial late game advantage.

Like everything in the TEC arsenal, it's awesome if you bring it out early, and gets worse as the game drags on.  When you first get ahold of it, it's the strongest superweapon, but once you reach the very late stages when money is no object it's (as you say) a waste of effort.

TEC's only saving grace in the late game is its industrial capacity.  If that's not enough to overpower the enemy, then there's little you can do. 

Nope, destroying orbital structures (and units, for that matter) is the effect of the Vasari superweapon.  The Vasari superweapon is godly to the point at which once a player has enough of them he's basically unstoppable.

TEC is still a powerful race, it's just they're more of an early-game race.  Hit that same Advent near the start of the game before he gets his high level tech and TEC can really pound the living daylights of them. 

The problem is not so much that it's impossible to win as TEC in the late game (because it can be done) but rather if you had actually had those kinds of superior numbers, you should have already won.

If you were only just matching the Advent or Vasari in the mid-game, when TEC advantages are still relatively potent by comparison, what makes you think you have any chance in the late game when TEC advantages are diminishing and Advent/Vasari advantages are growing?  Simply put, the TEC's time to shine is in the early-game, and any advantage they carry into the late game is what they earned early on. 

If you weren't good enough to actually gain an advantage in the early game when TEC is at its finest, how do you expect to do so in the late game when TEC is simply outmatched?