There are lots of people who have a rather simplistic approach to nutrition and think that removing fat and calories makes you healthy. Then they go through recipes for things they want to eat, replace the sources of fat with something which doesn't have fat and doesn't make the result outright inedible, and declare their recipe a success. I think this is what happened here.
In a cake, eggs provide leavening, moisture, smoothness, own flavor, and enhancement of other flavors. Oil provides smoothness and enhancement of other flavors (and possibly its own flavor, if not netural). And while it is not water based, it keeps the moisture in the cake from evaporating, so it makes the cake less dry.
If you are a "simplistic nutritionist" without all this information, you can approximate some of the effects with soda. It will provide moisture, and it will also provide some leavening because it is fizzy. It will provide some flavor of its own too, but frankly, I find the rather chemical flavor of soda to be unpleasant. And it won't have any fat. In the eyes of the simplistic nutritionist, it has successfully replaced the oil and eggs while reducing fat and calories.
From the point of view of a baker, the cake will be a disaster, and won't even deserve the label cake. It will dry out quickly because it has no fat. It will have a bland flavor. Its texture will be terrible. They say "more chewy?" It will miss both the protein structure and the emulsifying agents provided by the eggs. It will be essentially an overwhelmingly sweet quickbread with no redeeming qualities. From a culinary point of view, it will be terrible.
Bottom line: under some assumptions, it is a good substitution. For me, these assumptions are so far from reality as to be useless. It is a terrible substitution.
Frozen spinach has been boiled/blanched. You can do this if you really want it to be as much like frozen spinach as possible, but really, you can just cook it with the water left on the leaves from washing - effectively a bit more like steaming. There's no need to freeze it. This will result in something with fresher flavor and a bit more substantial texture than frozen spinach (not as eager to disintegrate). And you don't have to worry about moisture much - a lot of the water will cook off - but you can certainly drain it additionally if it's too much for you.
If you really want it exactly like frozen spinach, you could boil it, and maybe even freeze it to help mess up the texture, but I'm guessing you'd prefer cooked fresh spinach anyway. In this case, you'd have to squeeze and drain it just like with frozen spinach to get the water out. (If it's unclear how to do this, see What is the most efficient way to squeeze water out of cooked spinach?.)
Based on nutrition facts for raw spinach and frozen spinach, one 10 ounce package is approximately the amount you'll get from cooking a 340g (12 ounce) bunch of spinach - that weight is probably after removing the stems you're not actually going to cook, though. This fits with my experience cooking down spinach. Most things you'll use it in are really forgiving, so probably best to err on the larger side with your bunch of spinach!
Best Answer
According to stevia.net one tablespoon of stevia (in powder or liquid form) is the 'equivalent' of one cup of sugar.
Similarly, lowcarbdiets.about.com tells us that sorbitol is 60% of the 'sweetness' of sugar.
Using sugar as a common denominator, 1/2 cup of sorbitol = .83 cup of sugar and so you should use ~.83 Tablespoons of stevia to gain the relative sweetness.
That calculated, I would mix 1 tablespoon of stevia with 1 cup of unsweetened applesauce and then use 3/4 of a cup + 1 tablespoons of the mixture, and then adjust from there.
Conversions like this are admittedly 'imprecise' but this should give you a good approximation to start from...your mileage may vary.