Kalnchoe baharensis. It can get some size.

Yep, kalanchoe beharensis 'napoleans hat' ... i have one about 3 feet tall, can take full 100 degree heat and thrives ... yours looks like it developed a nice trunk (if thats what that is ) hope you enjoy petting it!

so, the shadow from another bigger plant is the reason he grows somewhat horizontally? Like he is chasing the sun? Would he be happier if I moved him to a spot with maximum hours of full sun?

Probably, but only if you increase its additional exposure gradually.

Keep in mind this plant only keeps a few leaves at the top. It sheds the others as it grows. Don't think the plant is dying when the lower leaves dry. Also, like any Kalanchoe, they grow easily from a single good leaf so you can start new ones when the first one gets leggy.

Do you propagate from leaf same as with cuttings? i.e. cut leaf close to attachment point as possible, allow to callous, place in soil, and wait for roots to develop?

If given the environment it likes, it can attain some size. Check out the google images. They can get way above your head.

The plantlette will form on the leaf edge. keep it misted.