Hello! You definitely want the artist to cut the parts for you, because the parts behind what was cut will need to be redrawn otherwise, and you'd want the style to be consistent. It should be done in Photoshop, yes.
Ideally, the artist should create the body parts separately. Not a whole drawing, which would be harder to cut later.
You can choose to have skins that contain complete characters or skins that have just the outfits. The first is useful if you're just exporting videos or gifs, the latter is great to recombine at runtime.
The rest of the art goes into that [slot] folder, either as a plain layer, or as a group with the [merge] tag (that will be exported as a single png file just as if it was a single layer)
More about the mentioned topics:
Skins: Skins - Spine User Guide
Photoshop to Spine documentation: spine-scripts/photoshop at master · EsotericSoftware/spine-scripts
A video series that demonstrates the process from assets creation to rigging:
Spine Twitch Streams - YouTube
