An emergency leave application is written short and sent immediately. State that it is an emergency, give the dates as best you know them, and say you will confirm your return date as soon as you can.
Planned leave usually needs one to four weeks' notice depending on company policy and how long you will be away. Sick and emergency leave is notified as soon as you reasonably can.
For annual leave, generally no. For sick, emergency or statutory leave you may need to state a category — but not private medical detail.
Your line manager, with HR copied. HR records the entitlement; your manager approves the cover.