"...Incorrect arrow weight (spine? Can't remember the term) for the bow..." That'll cause the arrow to break when it hits.
If the arrow doesn't quite stick and hangs down or sideways, you're either following the string or not coming to full draw. The former is you holding the string as it goes forward. The latter is releasing before you're at full draw. Both will cause the arrow not to have enough speed. Left or right doesn't matter.
Push the bow away from you, while you pull the string, as you raise the bow to eye level. (This is easier on your back and shoulders too. No raising the bow and pulling the string. That will hurt you and you're not using the right muscles. Back and shoulder muscles, not your arms.) At full draw, with your string hand anchored in the same place every time, aim or concentrate on the target(depends on if you have sights or not. With no sights, use the arrow head as a front sight.) relax your string hand without moving the bow until the arrow hits. The tendency is to move the bow to look. Resist it. The arrows will go off to the right I think for a leftie. Your stance can keep the string from whipping your arm too. Stand so the string doesn't hit your arm. This is easier to do than write about. Basically, you're changing the angle between your arm and the string.