Guidelines for Names and Titles: The salutation should typically use the person's last name, along with a "Mr." or "Ms." In general, avoid using "Mrs." or "Miss" unless you are certain of how the woman wants to be addressed. When in doubt, default to using "Ms."
How do you know for sure whether or not to use a closing? One good test is to ask yourself whether this email is more akin to an instant message/text or a business letter. If you're giving your teammate a quick update on an ongoing project, a formal closing might not be necessary; if you're throwing your hat in the ring for a promotion, it definitely is required. When all else fails, and you're still not sure, err on the side of caution and include it. You'll never go wrong by being too polite and respectful.