Only "during" for both. In sentence 1, "over" implies that she was so loud, she made the performance hard to hear.
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lucas21cf her sneezing was so loud and often that I could barely hear the performance, can I say 'she sneezed over/throughout the performance' to express that unpleasant feeling?That feeling is not carried within the written sentence. Tone of voice and nonverbal expression may convey it.
lucas21cIn sentence 2, "over" implies that he could not bear silences in a conversation.]My remark means that he did not like silence, so he left.