Must a mother observe the waiting period (iddah) if a non-mahram relative enters upon her and offers condolences in the presence of her son?

If your mother's conversation with the young man was within the bounds of Islamic regulations, then there is no harm. Otherwise, she must repent. This conversation does not affect the 'iddah (waiting period); the 'iddah is ongoing, and your mother is not required to restart it.