The best answer would be "regarded" because of the word "curiosity". It was the first time the students saw their new teacher and they were trying to form an opinion of her (e.g. Was she going to be friendly, professionalism or helpful? Was she knowledgeable and competent in her teaching? What was her background?). So, the students were curious about her and perhaps looking at her demeanour to form an opinion of her. We often use phrases such as "regard (someone) with (a feeling/attitude)" such as suspicion, favour, fondness and so on.
As I mentioned earlier in your other post, we "observe" when we look purposefully in order to learn something. This word would be more suitable if the sentence were: The students "observed" how their new chemistry teacher perform titration to determine the concentration of a solvent." "Watched" can also be used here but the meaning of discovery and learning may not be so obvious.
Lastly, "watched" would be more suitable if your sentence were: The students "watched" (not "observed" nor "regarded") in delight when their 75-year-old chemistry teacher jived to the beat before doing a somersault.
I hope this helps.