First Question, before I start amassing walls of text before you:
Vanilla, Entrenchment, Diplomacy or Rebellion [beta 1]?
But, some basics I can answer: (Bolded/Underlined important parts)
2) Just because you upgrade the maximum number of Capital Ships/Fleet Supply you can have, does NOT mean you MUST own the maximum number of ships possible - and trying to do so immediately is pretty foolish, even as TEC. If you dont have the resources available to do so, dont spend it all in one place - make sure you are keeping pace with Research and Planetary development. You could have the largest fleet in the galaxy, but if you can't maintain your planets or research, your ships will crumble to smaller enemy numbers and your planets will fall into disrepair. Balance is key.
3) If you have the resources and you dont plan on a mass expansion into new/enemy territory, ALWAYS keep research going, but if you're hard pressed for credits, follow what you need. If your economy is sagging and you're not under the knife, invest in economic things such as trade tech, population + tech and resource extracting tech. You'd be suprised how quickly small numbers like 5% add up.
4) Depends on YOUR play style and YOUR first cap. Generally as TEC, my first cap would be a Sova Carrier (TDN Salvacion) or Marza (TDN Panzer), the former for it's economically aiding abilities, the latter for pure strength. To make up for a lack of an Akkan, I'd have two Colony Frigates. Generally, both cap ships would be able to clear out a planet's defenders alone, the Sova with the help of Missile Batteries (Fantastic ability in small engagements), the Marza with Incendiary Rounds/Radiation Bomb (the Vasari ships completely fail to match the destructive power of the Marza, imo.. both of these are great at taking out enemy ships en masse). A second cap for me would roll out around the same time that I was expanding too fast or fighting too hard for just one to handle. But if your first cap ships is an Akkan, your second should be something with strong firepower (NOT The Kol - it's a good ship in small engagements but it's abilities cost so much AM and do very little for a large fleet that I almost never build them) to attack/defend your holdings accordingly.
5) Oh, boy. A big one.
Vasari -
Skirantra Carriers - My first cap as Vasari AND a fantastic support ship, this baby can single-handedly produce up to TWENTY bomber squadrons on it's own. Past level 6, this ship can also make 3 copies of a friendly frigate - which means that 1 Karrastra can turn into 4 and take you out that much faster. Even at low levels, it can give off a large repair field which heals ALL FRIENDLY SHIPS TO IT IN THE REGION. Take this ship out ASAP.
Kortul Devastator - This ship is amazing at keeping itself alive while dishing out massive damage and crippling your anti-matter supply while doing so. Take this out while it's at low levels, unless you want it eating half your fleet alive.
Vulkoras Desolator - less dangerous than the other two, but it can raze a planet before you can say "Splendiferous".
Serevun Overseer - supports the bulk of the Vasari fleet and can slow down your reinforcements while boosting enemy strength.
Jarun Migrator - sneaky devil can build Starbases.
Advent -
Iconus Guardian- No, I'm not crazy for putting this in front of their Capital Ships - this thing is a MENACE. In fact, most Advent capitals are normally disregardable because the true strength of the Advent lies in their fleet synergy, and this unit takes the cake in terms of support. Any damage done to a ship when this angel of protection has it's Shield Projection/Repulsion on (You cant miss either really, they're the most obvious special abilities in the game afterSuperweapons) the ENTIRE FLEET under that shield shares damage evenly. So, if you're doing 100 damage to one shipunder a cloak, and their fleet has 100 ships, you will do about 1 damage to each ship. KILL ALL OF THEM FIRST
Halycon Carrier - interchangable on the list with the Skirantra, it boasts more Strike Craft than any other ship in the game, and a great support ability in that it can literally repel enemy squadrons from a large vicinity around it. Be careful around them, they're strong in small and large engagements.
Radiance Battleship- cripples anti-matter dependent ships (Such as a Marza, Dunov or Kol) and forces ships to attack itself. Less dangerous later on, but still a force to be reckoned with.
Illuminator Vessels - called Lums or Illums for short, they have long range, can fire from 3 of 4 sides of the ship and are spammable. Enjoy watching this fleet of piranhas eat your fleet tho, they're quite pretty.
Aeria Drone Host - more mentionable than the Vasari small carrier because it can have 3 squadrons and is, overall, the strongest small carrier in-game.
7) Armor, Shields, Autocannons, but ESPECIALLY Health (with the +).
9) Early for some, later for most. Early on there is a TEC Tech (can't remember the name) that reduces the cost of building Mines by up to 40% - which will save a TON of credits early game. (It's also not a bad idea to invest in an Akkan's colonize ability instead of it's passive one early on, saves you precious credits) I invest in that first. Max population techs are generally mid-early game, as is culture. You want to start spreading culture as early as YOU can, but dont rush for it. TEC culture is normally strong enough to hold it's own. Trade bonus techs are generally mid-late game, when you have a stable trade economy.
10) Depends entirely on you. Some players build up large fleets then rush for the enemy homeworld early, because the loss of a home planet early game is pretty much game over for whoever loses it, even if they can reclaim it.
Xer0 \^/