I want to write a letter to the admissions office of a foreign university, but I don't know the gender of the recipient. What should I call it?

I don't know the gender, so the address says: "to the relevant personnel"

I don't know what you want to express in your concluding remarks. If you want to apply for a school, it may be useful: "I would appreciate it if you could consider my application. I look forward to hearing from you."