1. The phrase 初めまして (hajimemashite) is used when meeting someone for the first time that you anticipate to have an ongoing relationship within a professional, personal or social setting.
2. The phrase よろしくお願いします (yoroshiku onegaishimasu) can have several meanings including:
A) I look forward to working with you
2) I look forward to getting to know you
3) I’m counting on you (When asking a favor of someone)
3. よろしくお願いします has multiple formality levels as shown below: