Can either HeroForge or HeroLab allow me to mix and match?
With Hero Lab, you can add whatever custom content you want. So you could add the Warforged and Catfolk races, as well as any classes you might want. This applies equally to published material as well as home-brew material.
We have an active community on our forums that have been adding and sharing content for d20, and they've already begun discussing the same for Pathfinder.
Do either of these products have something where I can enter my own adjustments?
You can also readily customize built-in content (e.g. core classes), as well as modify content created by others. So if you want to change the a class to a different hit die type, you can do so. If you want to change the damage of all longswords to 2d4 instead of 1d8, you can do so.
So as I see it, any software needs to utilize the Pathfinder Core Rules as its background, but also have other classes from other sources. I do see how this could cause a problem with some classes - such as the Euridite, where it is a d4 hit dice and of course uses 3.5 skills. So I would either have to be able to "copy" the class and be able to make a EurditePRPG class changing the hit dice and skills. Of course, being able to provide this new class to others would be important (but I'd assume that aspect, since the Eurdite is from Complete Psionic so other fans would have already had to create the class and share it).
That's exactly how Hero Lab works. When using the Editor, it's easiest to start by copying something similar to what you want. Then you just make the necessary tweaks. So there is no need to recreate everything from scratch. Although you are able to do that if you prefer.
Of course all this is a fairy tale and very unlikely, but wouldn't it be great?
Not a fairy tale at all. It's how Hero Lab already works.
One caveat: We had just over a month in which to fully implement the Pathfinder Core Rules. We didn't get everything finished in time for GenCon, but folks on our forums said they would rather have the data files early and incomplete instead of waiting an extra couple weeks. So we released early. However, the *last* thing we add, after everything else is in place, is the Editor. This means that the Editor for adding custom content won't be available until next week, when we release a free update with the stuff that is currently missing. If you want to take a look at how editing will work for Pathfinder now, please grab the d20 data files and take them for a test drive in demo mode.