If the Time was truely due, one can pray even if the athan wasn’t called. In Hanafi masjids, they delay Fajr and Asr prayers. One can pray before them as per the majority of Muslims.

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If you forget the qunoot in witr, you can continue your prayer without doing it. Kindly refer to the following link(s): Is qunoot mandatory in witr? https://www.youtube.com/watch?v=C-Im5zQVnQQ

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What you had missed, what you prayed after it takes its place. This means you have to stand up and pray one more rakah and offer sujood assahu after Salam.

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