Good set of questions. Let me see how I can help.
1. For this sentence, all you have to do is to answer the question - Who's driving? - The answer would be "She's driving" wouldn't it be? Therefore the answer would be She and not her.
2. The second sentence would have been right if it had been "The administration wasn't very happy with us". However here the sentence tries to say that the administration is not happy with SOMETHING about us - So it would be "The administration wasn't very happy with 'we stealing the mascot'.
3. This is about parallelism. Here you are comparing 2 people (He and He). So the right sentence would be He didn't think the coach was as smart as he WAS. We have neglected the WAS here because it does not make any difference.
4. Think about this sentence like this - "No one knows about the plot except You and me". Hence "me" would be the right usage.
5. The logic of the third sentence applies here too. The sentence would have to be "I can't handle stress as well as he can" - Here we are again neglecting the can because it doesn't make a great difference.
Hope that helps!!
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