What is the legal (Shar‘i) position regarding two divorces that occurred while the wife did not inform her husband of her pregnancy or menstruation until after the 'iddah (waiting period) had expired in both cases, given that these are the second and third divorces?

Divorcing a pregnant wife and not informing her of the pregnancy does not prevent the divorce from taking place and being valid. If you divorce her while she is pregnant, and you remarry her after her 'iddah (waiting period) from the second divorce has expired, without her having married anyone else, then she returns to you, and the remaining divorces are counted against her. Consequently, if you divorce her after that, it will be the third divorce, and she will be irrevocably separated from you (baynunah kubra). She will not be lawful for you again unless she marries another man willingly, and he consummates the marriage with her, and then he divorces her or dies, and her 'iddah ends.

The fact that she was menstruating does not prevent the enforceability of her divorce according to the majority of scholars.