Looks like dragon fruit = Hylocereus undatus. (It could be Stenocereus, that is very similar). Hope you have lots of room, they grow large and should be staked and tied to be more manageable. (I got rid of plant I had because the size and very sharp spines :)

They can be grown from seed. This plant is also used as a rootstok for grafting and could start growing , especially if grafted plant dies.

Yes, it's Dragon Fruit!

Complete with aerial roots which want to grasp something, as it's a climbing, vining cactus.

Jeff--- It's interesting that in nature there are a lot of patterns and repetition; apples grow on apple trees, oranges grow on orange trees and dragon fruit grows on.....?

I got confused by the two. I think it's Orchid Cactus (disocactus x hybridus).

I do not have orchid cactus, but believe it has flat stems, with scalloped edges and I believe no spines? IIRC, it doesn't need strong sun. Hylocereus is generally 3-sided, has nasty spines, and many aerial roots - very visible in op photos. It tends to undulate with age, grows fast, and likes lots of sun and warmth...If left untrimmed, it could reach many feet in length - like 30...