Is ghusl valid despite these whisperings and thoughts, and is beginning ghusl valid with these feelings?

The cure for obsessive thoughts (waswas) is to ignore them and pay them no mind. Whenever an obsessive thought occurs to you, dismiss it and proceed with your worship. When performing ghusl (ritual bath), do not hesitate with the intention. Begin the ghusl immediately, certain that you have made the intention for it. Then, pour water over your body in a way that you are reasonably sure the water has reached all parts of your body. Once this is achieved, put on your clothes and go perform your prayer. Do not be bothered by any doubt that may occur to you afterward. Doubt about an act of worship after completing it does not affect its validity.