Figure Skating/Blade sharpening and falling
1) is falling typically related to blades which are in need of sharpening?
2) How can a layman ( skater's mother) tell if a recent sharpening was not done properly?
3) What are some problems which would manifest themselves while the skater is on the ice if her blades are not sharpened properly?
A blunt edge in need of sharpening does give less margin for error, and therefore will increase the frequency of falls. It is rarely the only reason for falling. It is more often faulty skating technique that causes falls.
A lay person can check the levelness of the edges by balancing a pencil or pen across the upside down vertical blade. Too little levelness precision is the most common and most noticeable sharpening error. If the levelness of the sharpening is not precise, one edge will feel sharper than the other. It is difficult for a lay person to ascertain the radius of hollow of the sharpening without a special gauge. Smaller radius means sharper blades and more sideways grip, and, with it, the ability to save some falls. Less flow is the trade-off for that deeper hollow.
Improper sharpening will make it difficult to skate in a straight line with weight properly distributed on the skating foot. It may, for example, require the skater to have more weight under the big toe. Sharpening is not the only cause of this difficulty, however. Less-than-ideal blade mounting, can also be to blame.
I hope this helps you understand equipment better. It is not easy to diagnose equipment problems. All the best!