Okay, so I've never actually done improv. But one of the basic principles is that you're never supposed to deny and offer made by your partner. If your partner says "I just bought a pet zebra", you don't say, "No, you didn't buy a zebra" because that leaves the scene with nowhere to go. Instead, your partner says "I've bought a zebra", and you say "I asked you to get my cough syrup and you came back with a zebra?". The basic point is that negating something is boring, as is simply accepting it. What you want to do is accept it and then add onto it; this is the "yes, and" principle. With every additional thing you add, you increase the complexity and give more to the scene.
I was thinking about this because I'm working on a new setting and trying to tear apart other settings that I enjoyed to see how they work. Worm is a big one. The most interesting powers within the setting are built on the principle of taking something basic and adding on a restriction. Burnscar has pyrokinesis; yes, and the more fire there is around her, the less control she has over it. Battery has super speed; yes, and she has to charge it up in order to use it. Trickster can teleport things; yes, and he has to swap two things of similar mass.
This is one half of Sanderson's Second Law; limitations, costs, and weaknesses are more interesting than powers. But Sanderson is explicit that his law is not just about creating complexity, it's about forcing more interesting things into the story. I think where I disagree with him is that I think limitations are about complexity and that's most of what makes them interesting, meaning that it should also be possible to add complexity (and therefore interest) if you use an additive rather than subtractive process. I guess I would also add that whether something is an addition or a subtraction is largely a matter of perspective.
Take something like Avatar: The Last Airbender. There are people called firebenders who have short-range pyrokinesis; yes, and they can shoot lightning if they have the right training, yes, and their power increases tenfold when a particular red comet crosses the sky. These things are additions to the core conceit, powers added on top of powers, but because they add on a complication, they add on interest and make things more compelling. We might imagine a simple magic system where mages can control and manipulate glass; yes and there are mages that manipulate sound. This is instantly more compelling, because we immediately set up a conflict and contrast between the two systems of magic.
To some extent Sanderson does this within his own magic systems. Mistborn has a system of sixteen feruchemical abilities and sixteen allomatic abilities and much of what's dynamic and interesting about the industrial era books is how twinborns (which have one from each set) can combine their abilities in unique and interesting ways.
Precognition. Yes, but happiness.
Given that it's a "but", there's an implied limitation. So, the ability to see the future, but limited to only happy things, or possibly only while happy, which might amount to the same thing. As soon as you start looking at something that makes you upset, the vision starts to destabilize.
Emotional manipulation. Yes, and age.
Emotional manipulation is one of those things that's pretty damned wide. The word "and" means that we're adding something onto it, not taking away. Emotional manipulation getting stronger with age feels a little too simple, so maybe we can tie this manipulation to age in a different way. Perhaps negative emotions are tied to getting older and positive emotions are tied to getting younger?
Earth manipulation. Yes, but heat.
Earth manipulation probably means being able to telekinetically move rocks around, though there are a few directions you can take that end of the prompt. Heat as a complication might mean a lot of things: earth manipulation gets more difficult as the temperature increases, earth manipulation generates heat, earth manipulation requires heat as an input, etc. I think I like the first one better, since it brings to mind an earth-mover who stays in colder climates and shuns the fires of civilization.
The generator is not robust and probably has some nonsensical combinations. Each of the lists could probably be expanded in size two or three times over to give more interesting combinations, and weights could be given to the powers and modifiers that are most open to interpretation, or with cascading probabilities. But let me know whether I'm just blowing smoke; I'd love to see some examples given the prompts.