Hi, I have two questions about the original TI3:

1) There is a secret ovjective (Keeper of Gates I think) when you have to control all systems containing wormholes. But what happens if there aren't any? (e.g. in a 3 player game when the 4 removed random systems were the worm holes) Do that player immediately score 2 VPs?

2) There is a law which lowers the space docks' unit limit to 2 if accepted. How many units can you buy if you previously researched Enviro Compensator? (2 because the law states that or 3 because of the tech?)

The FAQ addresses the second question. The order of precedence is as follows:

Political Cards, Technology, Action Cards

So you would be able to build 3 with enviro compensators.

As for the first question I can't answer that officially, but I would assume you would discard the SO before play started and draw a new one as you would with Political and/or Action cards that cannot be played due to Strategy Card set chosen.

I 've got one more question:

The Initiative Strategy states that if a player chose that card before then he has to choose something else. But if we play 3 or 4 player game when we choose two strategy cards then at the beggining of the game the speaker may choose initiative and another powerful strategy (e.g. warfare) and remains the first player. So I think it is a bit powerful in a 3 or 4 player game. Is there a rule for that? IMO the first person with the speaker token shouldn't choose initiative strategy.

There is nothing to prevent that from happening in a 3 or 4 player game.
However, if you are playing with the Imperial card as written, it would not be smart to pick the Initiative card first.

In the original Strategy Card set, Imperial is the card YOU MUST PICK IF YOU CAN. If you cannot pick Imperial you MUST PICK initiative.
If you do not do this "clock" you will be severely hampered in your efforts to win. The Imperial card is 20% of the required points to victory every time you get it. There is never an excuse to NOT take Imperial if you can.

If you are using another variant for Imperial, the disregard the above. But there is nothing stopping someone from taking Initiative as their first pick even if they are the speaker as long as they didn't pick it in the last round. (This can come up in 3 and 5+ player games as not all SC's are taken and Initiative doesn't have to be taken). It's powerful, but by picking Initiative if you are the speaker already you are losing out on the most powerful SC's as they will never make it back to you.

As Funky said, going first is indeed good, and can counteract the high-initiative numbers of some of the cool strategy cards. However, picking Initiative (or Leadership) as your first pick often means that the other players will snag those good strategies before you get a chance to pick your second one.