Need help with identification and propagating

Got this baby from a local nursery. It was in a terrible state no sunlight etioled bending leaves.

Don't have a lot of experience with succulents but I've been giving it plenty of direct sunlight keeping and it under a grow light too

Watering it very scarcely.

That's about it. No clue about it's name or how to go about propagating it(it shed 2 leaves)

can the propagating leaves handle direct sunlight (i live in a tropical region so the sun's pretty strong) or do i place them in a seperate container with soil under the light? And how long does it take to show any signs of new growth? What about water propagation?