Does a legal delivery depend on the arm angle with respect to the head?

With regards to the arm, this is covered by Law 21.2:

For a delivery to be fair in respect of the arm the ball must not be thrown.

A ball is fairly delivered in respect of the arm if, once the bowler’s arm has reached the level of the shoulder in the delivery swing, the elbow joint is not straightened partially or completely from that instant until the ball has left the hand. This definition shall not debar a bowler from flexing or rotating the wrist in the delivery swing.

So long as the bowler's arm does not straighten in the delivery swing, it is legal; the Laws make no reference to the angle of the arm with respect to the head.

There are of course many other ways a delivery can be a no ball, ranging from the very common (not having the front foot on or behind the popping crease) to the very rare. These are all detailed or referred to in Law 21.