Separate curved paths from one origin, not to append to existing path, in one layer

What I suggested is just on a plain layer, and the subpaths were stroked with a brush.

When you say Layer, I assume you mean a Shape Layer. If you are willing to use plain garden-variety Paths, you could do this:

Draw your first path with the Pen, and click on the origin point with the Direct Selction tool. Copyit to the clipboard, and paste it back. It will paste as the first segment, with two endponts. With th Direct Selection tool, select the second point, and then drag it some distance away. You need to do this as two seperate mouse moves — Click and release (to select), then click+drag.

With the Pen tool, click on the second point, to pick up the path. Now you can add points and modify the curvature of exiting segmnents.

Continue to paste and pick up path as may times as you like. You will end up with a Path that has several distinct Sub-paths that have their origins in the same location. You can then stroke the entire Path, or select each path individually with the Path Selection tool, and stroke them seperately.

PS essentially has no "snap to path/ anchor point" feature due to its tools' options being contextually auto-infered - if a path selected, it will always assume it's the one you want to work on whiule unselected ones are simply ignored. Sounds like you seriously need to move on to Illustrator or another genuine vector drawing program. It's simply beyond PS' capabilities. It was never designed to be a vector drawing program, after all.

Mylenium