Must I repeat the prayers in which I was unaware of the obligation of the opening takbir (takbirat al-ihram) and of the bowing/prostrating takbir when catching the Imam in bowing or prostrating, knowing that I do not count their number?

Whoever catches the Imam while he is bowing should pronounce the opening takbir (Allahu Akbar) while standing, then descend into bowing. The opening takbir is sufficient for the bowing takbir, according to many scholars. As for whoever catches the Imam while he is prostrating, he should pronounce the opening takbir while standing, then descend into prostration without pronouncing a takbir (for prostration), because it is not a place for a takbir of transition.

Whoever pronounces the opening takbir while standing and then descends into bowing or prostration without pronouncing a takbir (for bowing or prostration), their prayer is valid, although it is recommended to pronounce the takbir for bowing. As for whoever pronounces the takbir for bowing or prostration without pronouncing the opening takbir while standing, their prayer is invalid and they must repeat it. If they do not know the number of prayers (they missed), they should make up what they are certain will absolve their responsibility.