I always feel rapid heartbeat when laying down to sleep. Is this normal?

Maybe. Depends! Patients often feel their heart beats more at night, not because something happens to them when they lie down (though bad dreams and aggravation can cause palpitations!). It's usually a "signal to noise" issue, i.e., lying down in a dark, quiet room may "unmask" underlying awareness of heart beat because there's less external stimuli to interfere. Talk to your doctor to check 24° rhythm.
Yes. I see this often in patients, its unclear what is going on, but i think it may sometimes be related to the fact that when one lays down, more blood flow reaches the heart from the feet and causes the heart palpitations. A solution may be to first raise legs in a chair for 15 minutes then lay flat. Would be curious to know if this helps. Of course, one should rule out heart disease or svt ct.