No. Layers are stored as shape keys, and shape keys cannot hold Multires data. Apply the Multires modifier (or subdivide the mesh) first, then create your layers. Detail lives at the mesh's real vertex resolution.

Not once layers exist. Each layer stores a position for every vertex, so the vertex count has to stay the same. Do your topology work first, then add layers. The panel will warn you if the topology changed.

The most common causes are that the layer is hidden, its strength is zero, or the wrong layer is active. Hidden and zero-strength layers are locked on purpose. Click Sculpt on Layer to reveal the layer at strength 1 and enter Sculpt Mode on the correct target.

Two or more objects share the same mesh data. Layers write into the mesh, so shared data could change other objects. Click Make Mesh Single User in the panel. It copies the mesh and its shape keys.

Merge Down combines two layers into one and keeps the result as a layer. Apply / Bake adds a layer's current result to the Basis and deletes that layer. Both keep what you currently see, so hidden layers and masked-out detail are dropped. Undo can bring them back while your history exists.

The layer stack is meant to be kept unanimated. If shape key animation or drivers exist, Delete, Merge and Bake are blocked because baking at one frame would break other frames.