To make a rope ladder with vellum, can you use a 3D model or is it done another way? I am wondering how to use apply textures.

If you can use a 3D model, do the rungs have to be attached to the side ropes as a single mesh or can they be separate pieces that are not attached and still be constrained together?

Several ways to go about doing that. A common method is to create a geometry that closely resembles you final render geo in size and shape but is friendly for simulation. After the sim you can then pointdeform the render geo with all of its details, UVs, etc with the simulated simplified mesh.
The simulated proxy ladder could be one continuous mesh or be assembled and glued together from individual pieces without problems.

Thanks. By "glue together" is this done with glue constraints? I am new to vellum.

Or you could use weld.

Is "weld" a vellum tool or a general modelling tool in Houdini?