Not for a useful interview. If you tell me you founded and sold a machine learning company but can't explain the pros and cons of using variance versus standard deviation then you didn't sell a machine learning company.
Do you mean for measuring goodness of fit between a prediction and the known truth in training data?
If you want to assess the presence of knowledge, give a test rather than an interview. The interview is just a way to make it easier for the con artist to snow you.
What makes you think this? Anything aside from intuition?
But anyway, you'd get enough for a follow up question, but not really enough to pass. The key is that the sum of uncorrelated distributions has a variance that is the sum of the variance of those distributions. This isn't true for standard deviation. This is useful so we use variance when we think we're dealing with random variables. Standard deviation isn't as useful for intermediary processes.
Another follow up question - actually the first question in my head, but by a mental slip-up I typed out the wrong thing: Why do we use square error when absolute error would do?
The answer to this is actually quite illuminating because there are multiple valid but contradictory positions on it, much like the Bayes vs Frequentist debate.