How can I make sorbet without a recipe?

Too much to go into here, but let me refer you to Harold McGee's less well known book, The Curious Cook: More Kitchen Science and Lore, where he has an entire chapter devoted to this topic, complete with tables for a whole bunch of fruits.

Your question asks about a lot of very specific scientific detail, but really, with a bit of experience, you can make sorbet without any of that.

For most fruits, you need about 1/3 as much sugar as fruit by volume - two cups of fruit and 2/3 cup sugar is pretty common in recipes. This works with a good variety of fruits - for example, mangoes, strawberries, and kiwis should do well. If it's too thick, you may also want to add a bit of water, perhaps even up to the amount of sugar you used. With less water, you'll get a richer, more velvety, perhaps almost creamy sorbet, depending on the fruit; with more water it will of course be icier.

Of course, you'll end up adjusting the sugar sometimes - a bit less for very sweet ripe fruits, and a bit more for less sweet ones. But so much of the sugar is coming from what you add that you don't usually need huge adjustments; it should generally be somewhere in the 1:4 to 1:2 range. And there's enough variety just in the sweetness of the same fruit that predetermined ratios aren't always exactly right anyway.

If you make a few sorbets from recipes, you should be able to judge well by taste: before freezing, it will be quite sweet, a bit more than you'd want to eat. Unsurprisingly, it should be similar to the sweetness of melted sorbet, perhaps a bit more sweet than melted ice cream.

And as always, adding a shot of liquor will soften it up; this is handy if you find that sorbets softened only by sugar are too sweet for your tastes. Neutral things like vodka are handy since they'll work with any fruit, but sometimes this can also be a way to add an additional flavor. And if your fruit works with a wine - strawberry-rose and blackberry-cabernet are both pretty good - then using wine instead of water will soften it very nicely.

Finally, I noticed the juice vs puree point. I've never made sorbet with juice, but I suspect that'd be prone to being really icy. I've always used pureed fresh fruit; it'd have to be really good, fresh juice to taste as good as fresh fruit.

I have made sorbet twice without following a recipe, just guess and go. I made rhubarb sorbet and watermelon sorbet. You need to make sure you add a heapingly large amount of sugar, and at least a shot of alcohol. I did with 1 1/2 shots and it turned out find.

Doing this though, you will not get 100% perfect texture. It came out of the machine good, could have served it up like that, or maybe chilled an hour. After chilling 3 hours it started to become less silky.