Let's hit the issues one at a time.
First, I suspect that the white bumps are pearly penile papules and they are indeed nothing. They may go away with time and they may not. They are not an indication of anything and will not affect him at all. They are certainly not an indication for circumcision.
The pieces of tissue are remnants of the epithelium tissue. It's this tissue that bonds the foreskin to the glans in young boys and is exactly the same tissue that bonds your finger nails to the nail bed and is the only tissue in the human body that breaks down like this without replacing itself. there is no equivalent in females. This tissue is absolutely normal and the body will expell it over time. It certainly is not an indication for circumcision.
It is absolutely normal for a four year old boy to have some remaining normal and natural adhesions. They will break down over time and disappear. Again, not an indication for circumcision under any circumstances.
This doctor has shown amazing ignorance of the normal male body. All of this information is readily available and easily accessible even to the lay person. It is inexcuseable for a doctor to not have this information and is an indicator that he may be woefully behing on other issues. I would strongly recommend your cousin finding another physician who keeps up with current information and technology. Her son's life and health may depend on it.
Why don't you recommend that your cousin visit this forum? We may be able to be very helpful to her.