I use the same fertilizer that I use on my adult plants. I don't know how important it is, but it does have all of the micronutrients.

I always sow in mixes of moler cat litter and a small amount of something finer like sand, and add nutrients to the water. I don't use the "baggie method", but grow my seedlings almost like my adult plants, but with more shade and water.

The oldest hybrids in this group, like the one in my photo, have their main flowering period in December-January, so I do understand why they were called Christmas cacti. Newer ones flower about a month earlier.

Yes, some species have their major flowering period in spring. I had the common hybrids in mind.

Schlumbergera often flower in spring, and sometimes in summer as well, even if their main flowering period is in late autumn.The last spring flower on my Schlumbergera:

The blackened stem is dead. As juster indicated, cacti should be left dry for a week or so after repotting to allow the roots to heal, otherwise they are easily infected. Personally I let plants lie with bare roots for at least one day before I repot them.

apparently there are two forms of Hatiora salicornioides, one with shorter nodes than the other But still relatively uniform in length, I guess? I guessed at R. cereuscula because it grows long stems that ends in clusters of much shorter, slightly thicker stems, and your plant seems to by trying to...

Rhipsalis, something like R. cereuscula.

Why the "hundreds of tables"? My own plant database has less than 20 ...

I have used a fan in similar situations, it helps.