Hi, I'd like to help you with your question.
Although lack of sleep and food deprivation can cause hallucinations, it does not cause paranoia as you described. In order to come close, your family member would have had to have been without food or sleep for a longer period of time. And even then, he most likely would not have had so many symptoms that mimicked a mental health disorder. He also would have had more physical symptoms.
The symptoms you describe are consistent with Bipolar disorder. It is extremely common for someone with a serious disorder such as Bipolar to have very limited or no insight into their problem. And it is common for the person to stop taking their medication and not seek help for the same reason. They feel fine and see no purpose in seeking treatment for something they do not have.
The symptoms your family member had correspond to a manic episode in Bipolar. The lack of sleep and loss of appetite are indicators of manic Bipolar. The person feels similar to a normal person who has taken Amphetamines. So sleep and appetite are greatly reduced. This is an effect of his disorder and not a cause.
Most likely, if your family member was already diagnosed and was on medication, he may have needed an adjustment to his medicine. Medications are effective at a certain level for a while but then the body becomes used to them and compensates, making it harder for the medication to have the same effect as before on the symptoms. He may need periodic adjustments to his medications to help keep his symptoms under control.
Although you cannot make your family member get help if he refuses, you can educate yourself and other family members about Bipolar and the signs and symptoms of a manic or depressive episode. This will help you spot a change in behavior earlier and also help you be able to know when your family member is in need of admission to the hospital. Here are some resources to help you:
The Bipolar Disorder Survival Guide, Second Edition: What You and Your Family Need to Know by David Jay Miklowitz
Welcome to the Jungle: Everything You Ever Wanted to Know About Bipolar but Were Too Freaked Out to Ask by Hilary Smith
Loving Someone with Bipolar Disorder by Julie A. Fast and John D. Preston Psy D ABPP
You can find these books on Amazon.com or your local library may have them for you.
You may also want to contact NAMI- National Alliance on Mental Illness http://www.nami.org/ for support groups in your area as well as other resources to help you and your family cope with your family members illness.
I hope this has helped you,Kate