This is probably the most likely one. Specimen asked about may be too small and distorted to be able to tell very much more. Brighter, more humid situation is needed for best growth.

https://en.wikipedia.org/wiki/Hylocereus_undatus

It's hard to tell from that rather beat up sample, but I would guess an epiphyllum hybrid. These tend to have some often complex parentage involving Epiphyllum, Disocactus, Pseudorhipsalis and/or Seleicereus. Regardless, they are all considered "jungle" cactus (native to rain forests, not deserts) and are pretty easy to grow and care for. Will also tolerate a more typical peat-based potting soil than other types of cacti or succulents, more what folks use with other houseplants.

It looks like it used to be a "moon cactus", with a grafted piece of Gymnocalycium on top. The base cactus (Hylocereus) then grew a branch in an attempt to save itself.

Hylocereus seems to be the most plausible option here, I think it probably was a moon cactus! That would make sense knowing my dad, because they sell those at a lot of stores where I live. How should I go about replanting it and getting it healthy again???

Sue is right, it is 'leftover' from the Moon cactus. Gymno is dead (the grafted part on top) and rootstock - Hylocereus - lives on. I just disposed off of one (was not a moon cacti rootstock but dragon fruit, same genus, grown from seed) because they get big, have deadly (IMO :) spines and grow all over the place, and I do not have space for it. Air roots are very typical and could be cut off.

Echeveria is very etiolated.

They both can be grown well again if potted in containers with drainage hole(s) and in fast draining potting mix. I would be-head echeveria a start rosette again, leaving some of the stem with roots potted too - it may start growing offsets along the stem, like this plant:

They both need much more light they have been getting. Unless that is supplied, they will grow the same.

Apart from the dead scion being present I don't think epicacti (Epiphyllum hybrids) very often produce consistently 3-sided stems with full compliments of serious bristles. Before the dead scion was pointed out I could see this had the stiff, tough, heavy growth of the Hylocereus - which I have seen many times in Hawaii.