1) Carve planes don't have a transform or a gizmo currently. It's not a bad idea to give them one, but currently this wouldn't be possible. Maybe in a future release.
2) Probably a good idea to eventually implement, yes.
3) This is not possible due to limitations in max's displace pipeline.
4) I'm not sure what you mean by this. All meshes are inherently made of triangles, and the tyCarve modifier doesn't specifically triangulate any existing quads, beyond what is necessary. Perhaps you mean that carves should only generate quads? Unfortunately not possible. But you can use your retopo tool of choice to convert the mesh back to quads after.
2) Probably a good idea to eventually implement, yes.
3) This is not possible due to limitations in max's displace pipeline.
4) I'm not sure what you mean by this. All meshes are inherently made of triangles, and the tyCarve modifier doesn't specifically triangulate any existing quads, beyond what is necessary. Perhaps you mean that carves should only generate quads? Unfortunately not possible. But you can use your retopo tool of choice to convert the mesh back to quads after.