acronym
Yes, but only if it is the the terms of the President of the United States. Not if it is the president of a smaller company or association. If you use it as President Obama, or President Bush, it...
No, unless you are using it as the name of a place, but I somehow doubt that.
No, diabetic is not normally capitalized unless it's part of a name or title, such as The Diabetic Cookbook or The National Diabetic Association.
No. It's not a proper noun, that is a specific person, place or thing, or title.