Is it possible to have high blood pressure even if you don't consume a lot of sodium, don't drink alcohol, don't smoke and exercise regularly?

Yes. Salt intake, alcohol and smoking make matters worse, but a person with healthy health habits can get hypertension, in part due to genetic make up of the person. Wish you good health!

Yes, it can happen and it usually falls in category of secondary hypertension, i.e. hypertension is caused by another condition such as kidney disease, endocrine abnormality, etc.

The exact cause of hypertension is not known . There is a genetic component . Lifestyle/ other disease can contribute or be secondary causes . https://www.webmd.com/hypertension-high-blood-pressure/guide/blood-pressure-causes