When you have a heart attack, is it normal to feel palpitations and pressure?

Yes. Pressure and palpitations are common symptoms of a heart attack. There are many others too such as sweating, arm or jaw aching, feeling of doom, nausea, and anxiety.

Related Questions

Could my blood pressure and heart rate tell if I was having a heart attack or could it be normal even if I was having one?

Not reliable. Blood pressure and heart rate are variable during a heart attack and not reliable predictors of a heart attack. Rather chest pain usually on the left side should be evaluated right away.
Not always. Some people can experience mild heart attacks with little or no effect on their heart rate or blood pressure and also at times no pain especially if they have conditions like diabetes as well. Really need ECG and blood studies to confirm heart attack. Talk to cardiologist if really concerned.