1. Stay calm and when on the phone speak clearly, naturally and smile when it's appropriate (some say always smile but you can't always - how can you sound sympathetic whilst smiling?) Stay focused and understanding and most of all LISTEN. Customer service call taking is all about making sure you listen, get the facts right, write them down (or type them in to the CMS), repeat them to the caller to ensure you've got it right and then try to resolve the issue.
2. Write the email professionally - ensure the spelling is correct and use correct punctuation and sentence structure. It's not an IM. Pretend it's a letter because in fact it is. Business emails are formal, unlike personal ones.
They cannot expect you to know how to escalate a problem or hand it over. They primarily want to know how you are going to interact with the customer and essentially how you will portray them as a company. So make sure your every word - written or spoken - is both friendly and professional.
Good luck!!!