I have wondered about this, now if I trade high profile techs to my vassals or allies, is civ 4 like civ 3 was, where when you did this, all of a sudden EVERYONE has those techs because your vassal or ally gave them away to the people you didn't want to have them?
To an extent, yes. Civs won't trade away anything they consider to be a "monopoly tech" - important techs which few other civs have researched ("we don't want to start trading away this tech yet"). Of course, if you traded them the tech, you must have it yourself, so that's reducing the monopoly factor by at least 1. The monopoly factor varies from leader and to leader, and I think also from tech to tech. So, if you trade an important tech to a miserly leader, they'll probably withhold it from other civs until someone else gets it.
Another factor is dipomacy. Civs won't trade techs to people they don't like - again, depending on the leader, they might not want to trade with civs with whom they're furious, annoyed, or even cautious (for Tokugawa or Ragnar). Also, I don't think they'll ever agree to trade with their current worst enemy. So, the civ to whom you trade the tech will not trade it to people they don't like, but probably will trade it to everyone else. And the people to whom they traded it might be friends with the first civ's enemies, so next turn, they'll trade it to them. If you're playing with lots of civs, tech spreads very quickly. On the bright side, this does mean the AI occasionally get cross with each other for trading with each other's worst enemies.
I think all of that was right. I'm not 100% sure about the monopoly tech stuff, but hopefully someone else can correct me if I got it wrong.
Disregarding that: I think everybody puts the tech slider higher than 50%, meaning that beakers are less scarce than gold. That should mean that gold is worth more. On the other hand, beakers are more useful...
Not quite. In Warlords, at least, the tech slider itself doesn't really make gold or beakers more or less valuable than the other. You could set it to 80/20 one turn, then 20/80 the next turn, and the result would be the same as leaving it 50/50 for both turns. This isn't quite true in Vanilla, but it basically holds for Warlords. HOWEVER...city improvements change this. They change it drastically. If you have mostly science improvements, gold becomes worth much more than beakers. Each unit of gold can be turn into multiple units of beakers, due to the multipliers from libraries etc. Multipliers don't affect science or gold created from production (using Alphabet or Currency), so if you have mostly science improvements, you should build gold, not beakers, and set your science slider high. If you have mostly gold improvements (market, grocer, bank etc.), beakers are worth more than gold, and it's better to build beakers than to build gold.
Note that building beakers or gold directly with production (instead of getting them with commerce, the normal way) is usually a bad idea because it's inefficient. But it does illustrate the exchange rate between gold and beakers well.
If you stop building new multipler buildings, the silder rate doesn't matter (you get the 80/20 + 20/80 = 50/50 + 50/50 effect again). However, if you're about to complete a new library, set gold to 100% until it's finished, then set science to 100% for a while and feel smug for getting an extra 25% on all that science. Similarly, you might set science as high as possible shortly before getting a market, and *then* go back to building up gold.
Remember also that the AI probably doesn't think about anything I just said, and has its own strange way of deciding how much gold a tech is worth. I think it's partly to do with how many other civs have the tech and how much research you (or them) have put into the tech already.