When it comes to MP, the first 30 mins of gameplay usually determines the rest of the game. By that time, the players that are going to die have been identified (as in, there's already a larger fleet barreling down their front door) and fleets are starting to reach tier 2 or 3. Therefore, it is important to have a strong military early game, but this depends on your location. So, here's some general advice...
For Starting Fleet:
For TEC, the starting cap is usually the Marza because of Missile Barrage at lvl 6, which is incredibly useful against mass swarms. In addition, the Marza kicks out the most DPS at lvl 1 than any other TEC cap ship and is great at bombing planets with Raze Planet, which is useful in close combat to quickly rush an enemy roid or dwarf and catch your opponent off-guard. Downside with Marza is strikecraft, in which case you brought a knife to a gun fight. I personally always go Marza whenever I play TEC (which honestly has been quite some time).
Sometimes the Akkan is preferred as starting cap since it is colonizer for rapid expansion. Plus, lvl 6 Armistice is an excellent ability as long as you can micro-manage.
Spamming LRF's early game is pretty usual, as they have amazing range and are quick to research. The one thing that I see here of late is people forgetting the usefulness of Hoshikos. Back when I played TEC, Hoshikos made up about a third or more of my fleet because their mobile repair is different than Vas (Skintra or Overseer) or Advent (Domina). Again, it's early to research and cheap to produce, in addition to significantly increasing your fleet's durability.
The TEC have the best eco in the game. It's incredibly quick to research, so getting a good Trade system up and running is easy to do. However, depending on how close your opponent is, don't start trade because it will hurt your ability to create a strong military.
For your questions:
1. Not necessarily. You need to know how to counter properly. Since there are so many out there, I won't go into details, but if you have specific questions, feel free to ask.
2. Corvette spams are good for titan rush and to destroy constructors, but they are easily counter with flak or more corvettes. I have lately been using vett rush much more since I play AR, but you never want to have only one kind of ship in your fleet. Always have different ships within your fleet so that the enemy cannot build a single ship to counter.