2) Nobody cares how good your solution is, they care about seeing your thought process while solving it. They are likely waiting breathlessly to ask you follow up questions about your poor implementation that will further enlighten them about the way you think. It would be a downright shame to disappoint them by writing a great solution right away.
3) This is a legitimately big problem. Everyone responds to the pressure of interviews differently and it is definitely not necessarily correlated to their response to the pressures of the workplace. Ideally you would notify the interviewer(s) of your anxiety beforehand and they would be willing to work with you on either a short take-home (which a lot of people also hate for other reasons), or some type of working interview (which is often infeasible).
The original article was about a specific-language whiteboard problem, which is open to arguments about tooling and internet access, but many people ask these sorts of questions in terms of pseudocode, structured written english, or even discourse out-loud, and the goal is not to determine programming language or algorithm knowledge, but problem solving skills.
edit: phrasing
