If you have a history of high blood pressure, high cholesterol, & heart problems is it ok to take a tbsp of pure nonhydrogenated coconut oil a day?

No. Adding more fat to your diet makes no sense. High blood pressure and cholesterol with heart disease means that you are past taking small steps in your diet. You need to cut your diet down to less than 2000 calories/day and reduce your sodium intake to less than 2000mg/day. Then only foods you should be eating are fruits, vegatables and lean protein sources. Water should be your only drink.
No data. The problem today with the acess to the internet and the widespread missinformation is it's hard to know what to do or who to trust. The information on " natural " remedies often come from people selling the supplement. Without fda regulation the information doesn't have to be evidence based. The truth of the matter is you exercise adhere to an american heart diet as well take your rx ur fine.
OK. But not helpful. Treat your BP to goal. Exercise regularly. Other recommendations would be based upon your specific history of heart problems. You may benefit from a low dose Aspirin and or lipid lowering agent. Go to framingham risk calculator - online- to estimate your risk of heart disease and discuss with your physician.
Caprilic acid. Coconut oil provides caprilic acid which works as antifungal and helps with intestinal irritation which contributes to high bp. Caprilic acid can also work in chelating intestinal toxin removal, anti-inflammatory effect with high cholesterol - so it works - use this for oil change program for body - once a quarter give your body good oils like flax seed, sesame seed oil, borage, olive oil +coconut.