I'm so sorry for this VERY late response. I've been super busy and haven't been online in months. You use them with MCEdit. That's the only way I know of, although I've heard there are other programs to use with a schematic.
After installing MCedit, and placing and unzipping the schematic somewhere you will find them, load up a map in MCedit, click the "import" button, select a tree schematic, and then place it in your world. You can adjust the position, rotate, and mirror them before committing to a placement in the program, which helps you to make much more realistic forests with them. You can even adjust the scale, although be careful with that one, as it can deform the tree a lot.

And again, sorry for the very belated response!

Good question! Until now, I'd actually never heard of the Pawpaw, but it's been added to the "unfinished" list.

Well, I'm just starting to experiment with dealing with large fruit/flowers in trees, but there are two possible solutions for now: wool, or glass. A third solution would be using flowers, but I have yet to find a way around block updates. The American Mountain Ash, which I've already released, uses orange stained glass to represent the large clumps of berries that it has, and I'm going to update the Desert Willow from my southwest pack to have purple stained glass for it's flowers.

Since, this is a new experiment, I'd love to hear some feedback on how it looks. :)

For me, the download is working. Can you be more specific?

Keep in mind, the schematic folder download is labeled "Download Minecraft Map", which is something that PMC is doing now, unfortunately. I guess they're now assuming that the only thing people are downloading is maps, which is clearly untrue.