I didn't know that about the Dunov - clearly late game strategy (reminder: 99% of my experience is SP, not MP). I find the Sova to be quite effective once I get more flights of strikecraft. Maybe I don't get them but I think their lower level abilities seem useless to me. I never take embargo, and take the first 1 (forget what's it called I dislike it so much) when I can't take the 3rd one (can't remember it's name either...). I find the Marza to be very effective for planetary bombing, but other than that I tend to move it to the front to attract fire - I've rarely leveled one up enough to get missile barrage (although I liked it a lot when I did get there ). I'll have to look more closely at the Corsev. I've clearly not used it effectively when I have built it.
TEC capitalships in a nutshell.
Kol - 99% of the time, don't Build it! The only thing it's good for is flak burst. So unless your opponent is building nothing but strikecraft any other TEC capitalship can do what it can do better.
Akkan - Unless you get comfortable with rushing this should be your first cap for economic expansion. Not only is it's colonization ability the most profitable, but targeting uplink + LRMs can make a decent starbase counter early game if you don't have time to transition to bombers or Orgovs. Finally Armistice is one of the few TEC "wow" abilities, and can both let you bypass annoying defensive positions or more likely get your fleet out of a bad mess in one piece. Likewise, if you're losing this is the cap you'll need to rely on to migrate somewhere else in hope of setting up an Empire where your allies can cover you better.
Sova - This is the best cap ship for rushing and is a brutal brawler, making it great early game. The Sova rush isn't as game breaking as it used to be thanks to Corvettes, but if you can keep a Sova with embargo on the enemy homeworld from the start of the game you'll weaken his economy enough to win the war of attrition. However, you'll need plenty of practice with rushing in general to pull this off. Even if you don't go for this first, missile turrets and the fact that its a carrier means you can pull of the great LRF + Bomber combo early even without research. However, at time goes on the lack of any Area of Effect (AoE) or support abilities makes it less useful in large fleet battles, so you'll probably never build a second one.
Dunov - The opposite of the Sova, this support cap only shines mid-late game. It's indispensable for dealing with titan, as it's the only TEC ship that can drain an enemy titan's antimatter. It's other two abilities are great for screening your own titan, with shield restore keeping it alive and Magnetize to disable enemy caps like the Kortul, Radiance or another Dunov that might be trying to disable your titan. And for the Ragnarov especially, Flux Field is a boon that will allow it to reach its full destructive potential, as the lower antimatter costs should allow it to use all of its abilities at once.
Marza - The Marza is all about blowing stuff up. Yeah it's a good planet bomber without doing anything. But it also has some of the highest forward damage of any capitalship, making it great at focus fire. Radiation bomb isn't great but it is an unlimited AoE (I.e. it has no target cap) and is available at level 1. But the real reason for getting a Marza is to get it to level 6 for Missile Barrage. This is on the of the TEC's few 1st tier capitalship abilities. It can damage an unlimited number of ships in a circle around the Marza, and over the duration of the entire ability will do several thousand damage worth to each ship. If you opponent doesn't see you using it and doesn't move his ship or disables your Marza mid abilities, everything smaller than a cruiser will likely be killed by this ability (especially if you get the second level). For the TEC Loyalists especially, you need to learn to use this as their titan doesn't do a lot of unlimited AoE damage. For the Rebels their titan does an even better job, but the more AoE you have the better.
Corsev - It's better to just explain this one's abilities individually than to give it any sort of a role. On one had it can do decent damage to a single target with boarding party, and if this ability kills a frigate that frigate will be brought under your control. Even better is demolition teams. This is an unlimited AoE that kills one of your own ships but does good damage to enemy ships. Unlike missile barrage though, you don't need to wait for level 6 to get this one. Either use it on Corvettes or scouts for cheap fodder, or you'll do twice as much damage if you blow up an enemy ship you captured. Finally, this ship is only second to the Kortul as a tank. It has a passive ability that heals it every time an allied ship is destroyed, and apparently even with focus fire this can happen enough to keep it alive far longer than most caps.
This might be a difficult question for MP but do advanced players often max out their fleet capacity research? On medium and large SP maps I quite often do, but I don't think I max out on actual ship capacity (can't build more ships). Maybe I'm putting too much into fleet capacity when I don't need to. Did I mention I got a lot to learn. Gawd!
Most MP games do not last long enough for players to max out their fleet supply. Also keep in mind the fleet upkeep makes getting maximum fleet supply a huge drain on your economy. Definitely keep whatever fleet supply you have researched used up, but you need to be careful when you choose to expand it. Many pro players only expand it when they are in danger of losing. I'd say if you're routinely going beyond the 4th research of fleet supply you might want to consider if its worth the economic pain to do so.
That said, the timing on when to fleet up is probably one of if not the most decision you make in a game because its not reversible. And like all timing related decisions its on that only gets better with experience, exactly what the right move is will be different every game.