The white round things look just like slow release Osmocote to me. Osmocote pellets absorb water through semi-permeable membranes, filling with liquid over time. If you can pick up these 'pearls' and burst them, it's Osmocote. Of course, slug eggs look like that, too. ;-) Am still not going to weigh in on the blue stuff, but there is a crystalline blue nursery fertilizer commonly used in the industry. I've got some sitting in Weigela containers we purchased not too long ago, as we speak. I still can't make out the 'shell-like' things that you are talking about. But if they look just like a snail shell, then they ARE! With all of the fallen leaf debris in the pot, I wouldn't be surprised if there were snails. There is nothing that looks 'just' like a snail, other than a snail. The fact that your plant has obviously spent quite some time at the nursery is another clue that it might have become home to soil dwelling critters. I'd avoid using any chemicals on your plant. Don't see the need for it. If 'the blue stuff' is a fungus (don't think so), it's growing on the soil and not the plant. That means that fungicides are useless and uncalled for. Here is a link that might be useful:

There is no difference between stem tissue and branch tissue. They are the same & equally likely (or unlikely) to root. I also think trying them directly in the ground where you live will be very unlikely to yield results. Besides, the plant will prefer full sun and you'll not likely be able to root them in full sun, so you'd need to shade them or move them if the did happen to take. You should use a very coarse and sterile mix for rooting. Perlite, Turface, a combination of perlite and Turface, or any combination of chopped sphagnum moss (not peat moss - chop it in a blender or food processor) and either/both of the other two ingredients is particularly effective. If you use the coarse ingredients, soil volume is of no concern and a greater volume is easier to keep damp (but not wet). A spot with open shade is best (in shade but on the north side of a building or fence with open sky above). DO NOT fertilize cuttings until well after they've struck. Fertilizer inhibits water uptake (which is critically important to cuttings) and slows root initiation. Al

Thank you very much (especially naming the Jacaranda.) That one gives me terrible allergies. The last thing I need is to be growing it.

Do the black spots and clumps wipe off, or are they in the leaves themselves? Are they on the bottom of the leaf too? Do they feel different than the surface of the rest of the leaf (raised bumps, dry, or musby? I'm really not sure what they are, but the information will be helpful to others who are more familiar with plant diseases. The spots don't look like mite damage, especially because mites prefer tender new growth at the end of stems or branches. Check the backs of the leaves and that bud at the top of the tree for tiny dark red dots that easily wipe off or fall off if you shake or tap the leaf. They're really tiny, so a magnifying glass or loupe will make them easier to find if they're there. The brown areas on the bottom leaves look like classic signs of overwatering or underwatering by the grower, so here are a few questions: Does the pot have a drain hole? Is the soil very wet or just moist? What kind of soil is it--fine grained and peaty, or does it have larger grains that allow air to pass through the soil easily. Soil in the root zone can be saturated even when the top few inches feels dry, so stick a sharpened dowel, disposable chopstick, or a skewer all the way through the soil to the bottom of the pot to check the soil moisture. Fine grained water retentive soils can stay saturated long enough to suffocate and kill roots, reducing the plants ability to take up enough water, which causes leaves the plant can no longer support to brown and eventually drop off, beginning with the lowest leaves on the plant. The best way to deal with this is to repot the plant by removing all the old soil from the root system and replacing it with something fast draining and highly aerated, like Al's 5:1:1 mix made of five parts pine bark, one part peat moss, and one part perlite. However, there are ways to compensate for water retentive soils if you can't repot right away, including watering only when the plant needs it and tilting the pot 45 degrees after watering for 15-30 minutes to reason off most of the excess water from the lower part of the pot, as well as a few other tricks we can offer, depending on which way you want to go.