Fling is right on, the normal deceleration that we continuously perform during an approach requires about 2 to 3 degrees nose up, which makes the approach look steeper. Each degree nose up from normal causes about 1/2 knot per second deceleration.
The limiter to steepness is forward speed. If you are faster, the steepest approach you can make becomes more shallow, because the helo will only descend at a given amount to stay above autorotation. If you slow to 35 or less, the autorotation boundary is very far below your flight condition, so you can descend in full control at angles up to about 20 degrees. If you want to be steep and safe, be steep and slow.
No, Vortex Ring State is not possible in steep approaches, within normal reason (anything is possible for the truly ungifted pilot.)