Sometimes, when press against my stomach lining, I feel a palpation...What could cause this?

Aorta. Depending on where you are pressing, you may be feeling your aorta pulsing. Your aorta comes off of your heart and runs all the way down your abdomen before it starts to divide into smaller branches. The aorta is big, so it's not uncommon to feel it pulsing.
You are alive! Your stomach is a very soft organ. If you are not very obese, you can press on it and feel your aorta, the largest blood vessel in your body. This is very normal in young healthy people and people who are thin. However, if you are over 50, if you smoke or have high blood pressure or a family history of heart disease, then it might be a sign of disease in your aorta. Have a doctor check you out.
Muscle contraction. Most likely you are feeling an involuntary contraction of the muscles of the stomach or abdominal wall. If you feel it continuously, a concern for an aortic aneurysm could be raised. An exam by your doctor or an ultrasound or other imaging study could clarify this.