A leave application tells your employer what dates you will be away, why, and who is covering your work. The cover plan is the part people skip and the part managers actually read — naming a colleague who has agreed to take your handover is usually what turns a request into an approval.
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.