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.  

For Economy:

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. 

I recently played 1v1 against a hard AI on a tiny map (with 12 planets or so). You don't get a chance to develop an economy or do much research. You'll be continuously attacked by lots and lots of units and you have to keep building simple ships and keep countering waves and waves of ships. You'll have to be very careful about spending credits on research, trade ports and on building a Titan. I think such a game will give you plenty of practice in countering rushes.

I dont understand what this "rush" deal is. More often then not it is the standard opener used by experienced players.

To be fair I learned how to counter "rushes" just by playing cruel ai...

Things like Marza abilities and mass produced vettes would appeal to anyone who plays tec.

The only way to counter would be to put a lot of distance between the players-as HLT said- and to develope your science and economy.  I have always gone with science-then-civic research and switching to ports so you can afford the many fighter/bomber craft it will take to disable all those vettes and other tec ships that can do much damage early game.

The only way to get them off your back is to side with a storng military player early game and hope you can survive until you can get enough money and fleet.