You may not use all of those commands for getting your model ready for the further steps with Grasshopper. On the other hand, there are other difficulties and ways of reaching your goal. If you need an other Rhino command regarding meshes, please visit this site.
The MeshSplit command divides meshes into parts with another object, in this case your surface.
The ReduceMesh command decreases the polygon mesh face count while minimizing geometric and texture distortion.
The MatchMeshEdge command moves face edges of an open mesh to meet adjacent face edges.