Please post your IELTS essays under "Writing Feedback" forum.
.... well... in many officers subordinates call their managers by first name. But in a more official letter you address your bosses as "Dear Sir"
I'm writing to you to request some unpaid vacation next month.
My younger brother is getting married next month and he has asked me to be his wedding planner so, as the wedding planner I will have a lot to do like ordering the flowers, cakes, musician, photographers and videographers for the wedding. Writing and sending out the invitations of the weeding, also I have to help him pick his new suit from the tailor.
.... why you specifically say "unpaid"? Generally employees are allowed to exercise paid leave and they manage their committments within this entitlement. (i.e. paid leave)... So, my suggestion is not to specify what type of leave that you are going to apply as your prompt too does not specify it;I am writing this letter to inform you that I wish to take leave from work for 7 days with effective from 18th to 25th June in order to fulfill an important family commitment.
Now tell that your brother will be getting married and your family relies you on attending to wedding arrangements since they do not have support from any other person. ... You generally don't explain every activity that you have to perform, but gives the facts that justify your reason.