Your suspicions are correct. It is not an Echeveria. It looks like a Haworthia seedling. I'm not sure to what you are making reference that is a fungus. If it is that white fuzzy object in the center, that isn't a fungus. Maybe a closeup would define things.

Isn't this K fedtschenkoi? W/ its lovely pink highlight? So pretty. Sorry, don't know this behavior. There's a thread nearby asking about this plant. Is yours folded like that too Steven?

Denise, the reason your trees are not having Winter Leaf Drop (WLD) may be because you are keeping them cool and providing them with low light. The low light levels result in low activity of the leaves putting less of a burden on the roots whose activity is decreased below 50 F. In other words, you have found the right balance of light provided to the leaves and the temperature provided to the roots. The most likely reason that trees grown by others in the Miracle Gro Potting mix die within a short time while your tree survived is improper watering. However, Al Tapla would tell you that, by using Miracle Gro Potting mix, you are not letting your tree grow to its fullest genetic potential and that you should be growing it in the 5:1:1 or gritty mix instead. (I do not necessarily agree with him.)

Would anyone be open to sharing other examples of basal shoots on their roses, and what the buds (particularly the sepals) look like? The growth on my shrubs indeed seems to be coming from the base of the plants (not growing off another stem--at least for now), but the angular, elongated presentation of stems, leaves, and buds just have this "off" quality to them--but I am likewise a new(er) gardener, so I'm thankful for everyone's comments and input!