1) Do the abilities stack? For example, if I get 3 cruisers to use embedden or designate target on a particiluar target do I get the benefits from all three ships or just one?
Honestly, I'm not sure, but it shouldn't be hard to find out. Try it and take a look at the info card of the target ship - it should show you the numbers, so you can see whether the effects stack.
2) It seems like the TEC's abilities are very weak in comparison to the Avent's guardian's abilities. Am I right or am I just not using the TEC's abilities correctly?
I'd say 'different' rather than 'weaker', but your mileage may vary. Just bear in mind that tactics that work for Advent won't necessarily work for TEC, and vice versa.
PS: I read that each race gets a bonus for fighting in areas where they have the dominate culture. What are they?
They're earned through techs, and the techs explain what they are.
TEC get an antimatter recharge buff.
Advent get a mitigation buff.
Vasari get a damage buff.
The size of the buff depends on how many of the relevant techs you've researched.
