The cream whipper relies on gas expansion to work.
When you make whipped cream by beating, you beat fine air bubbles into the cream. The cream traps air and becomes essentially a matrix that holds those bubbles--a foam.
Your gas-charged whipper does the same thing in a totally different way.
When you charge the whipper with gas, there's high gas pressure inside with the cream. The cream will actually absorb the nitrous oxide you put in. Because of the pressure, the gas absorbed can be thought of as really really really small bubbles within the cream. So you have a matrix of gas and cream, but because the bubbles are so small, it's essentially just cream.
Chilled liquids more easily absorb gases at high pressure, which is why it's good to use cold cream and keep the whole unit in the fridge. A limited amount of agitation (shaking) exposes more cream to the gas, improving absorption.
When you release the cream from the device, the absorbed gas expands rapidly. The bubbles get bigger, and your cream to bubble ratio becomes more like the foam that we know as whipped cream. It's really exactly the same thing, only with nitrous oxide instead of plain ol' boring air inside the bubbles.
Why nitrous oxide? As I understand it, it's because it's the cheapest non-toxic, odorless and tasteless gas you can get. Carbon dioxide would almost be a good choice, but unfortunately it's bitter. Not a good match for cream.
Finally, why is shaking too much a bad thing? That one I don't know for sure, but I know what happens when you over-whip cream with the mixer. You make butter. Perhaps the gas or high pressure encourages this conversion, or maybe you're just churning it that much when you over-shake. Either way, I'm sure you've essentially made butter when you shook it too much.
A foam is just a liquid with plenty of air incorporated into it. You can incorporate air into any liquid; in order to be able to create an actual foam, however, you need to be able to incorporate the air faster than it escapes.
What makes a liquid able to hold the air you're incorporating (and hence form a foam) is a foam stabilizer, also commonly called an emulsifier1. I know of no specific taxonomy of stabilizers, but the vast majority are hydrocolloids AKA gelling agents and belong to some family of protein.
- Agar, carrageenan, alginate, xanthan, and pectin are all types of polysaccharide;
- Lecithin is mostly a random collection of phospholipids;
- Gelatin is denatured collagen, i.e. animal protein;
- Whey protein is the prevalent protein in dairy products;
And so on. Really almost any emulsifier will do. Basically everything in your list either is, or contains, one of the the additives mentioned above:
- Chocolate is almost always emulsified with soy lecithin;
- Eggs contain high amounts of lecithin;
- Milk and cream contain whey protein;
- Most "supermarket cream" also has emulsifiers like carrageenan already in it.
...you get the picture, I hope. The most basic answer I can give to this is that if you want to make a foam, you need to either use something that's already an emulsion (milk, butter, chocolate, etc.) or use an emulsifier/stabilizer additive (such as gelatin, lecithin, etc.)
If you want a relatively complete list of all of the food additives that qualify, you'll want to look at the E number, and specifically E400-499 (thickeners, stabilizers, emulsifiers).
1. As commenter Erik very correctly points out, an emulsifier is not the same thing as a foam stabilizer. However, by convention, the terms seem to be used interchangeably all over the place, to the extent that I get blank looks when I refer to a "stabilizer" as opposed to "emulsifier". So, know the difference, but don't get too hung up on it.
Best Answer
It's very difficult to create a firm anything with a cream whipper, since by definition what it does is whip. It's meant for preparations that incorporate a lot of air - i.e. light and fluffy. Most mousse recipes don't only use cream, they also use eggs and/or gelatin and that is what gives it its body.
There are certainly ways to whip things without cream - for a gel preparation (as opposed to a foam) you're generally looking at egg whites (or equivalent), gelatin, or carrageenan. Gelatin is already a very common ingredient in mousses, but I think carrageenan might be a better choice for what you're trying to do, because of its shear-thinning property; whereas with gelatin you have to heat it in order to loosen it up, carrageenan you can just shake a bit.
I think you'd do well to start off with a meringue-based mousse and forget the whipper, just to see if it's a texture you like. You make the base and then fold in the other ingredients. It's not going to be the same as a traditional mousse at all, but nothing will be without fat. Italian meringue has more of a frosting/icing-like quality, so you could try that as well.
Then you could try incorporating iota carrageenan (kappa isn't shear-thinning) or gelatin. I don't think I'd recommend a whipper for this, though. Typically you'd make this by first preparing the meringue, then folding in egg yolks and other flavours. The gelling agent would probably go in with the latter half, since I'm not sure if it's possible to whip egg whites with gelatin or carrageenan already incorporated (I've never tried, but it sounds dubious). If you do it in a whipper, I'm not sure how you could separate these steps. You could try to do them together if you don't mind the possibility of throwing away ingredients; my guess is that it might fail to whip at all, or if it does whip, then might be too thick to dispense.
You might also consider more traditional dairy substitutes - for example, there's a recipe for coconut oil chocolate mousse that you should be able to adapt to fruit. Coconut oil is a fat, of course, but I'm assuming your real issue is dairy - you don't explain your reason why you can't have fat or dairy and without details, it sounds like an unnecessarily arbitrary restriction - if this has something to do with not wanting a "fattening" dessert then it's the sugar, not fat, that you should be concerned about.
Anyway, one last thing - you probably will not meet with much success trying to use actual juice for this. I suggest using an extract and some food colouring if you want it to look right - or maybe some frozen juice concentrate, so you don't need to use as much. If you're whipping egg whites, you can't water it down, and you don't want to lower the pH too much either.