I am playing my first game with the Yor...does it do me any good to trade with another civilization for a tech that isn't in the Yor tech tree? Can I use any tech I trade for? On the trading screen I see the other civ's have techs with an asterisk by them. What does that mean?
I'm pretty sure you're talking about TA here rather than DA since DA still uses a common tech tree for all races. My experience with TA is rather limited so I can't answer this question. Hopefully someone else will come along that can tell you how it works.
Second, say I build a Fusion Power Plant (or something that increases by a percentage, not by points) on a tile that has a manufacturing bonus...have I just wasted that tile? Will the Fusion power plant still increase my manufacturing by 10% but not more?
Correct, building a power plant on a manufacturing bonus tile just wastes the tile same as if you put your manufacturing capital on a manufacturing bonus tile.
Also keep in mind that in many cases you get more production out of a tile by simply placing another manufacturing building rather than placing a manufacturing bonus building. When a planet has little production it's usually better to add another factory, once you already have a number of factories (or a factory on a 300% or 700% bonus tile) then an increase in manufacturing bonus is usually better. Just be sure to figure it out both ways to see which is better in each specific case.
And finally, I can't seem to figure out exactly how mining an asteroid belt benefits a planet. I am sure it DOES benefit the planet, but how? Does it increase MP?
I don't bother with asteroids myself, I believe they are too much work for too little benefit, however yes, once developed by a miner they do add to a planets MP/SP.
IIRC there are at least two or three levels of improvement you can make to an asteroid field that give corresponding increases to a planets production. The amount of increase is inversely proportional to the distance from the asteroid field to the planet. You can change which planet gets the production increase but I'm not sure exactly how you do that.
Personally I just find asteroids to be a nuisance so I select rare asteroids in the game setup and I upgrade my free miner to a colony ship and just grab an extra early colony. The upgrade costs 66bc IIRC and then I never deal with asteroids other than in systems that I've conquered and then it's just to direct the production to the nearest planet.