Does Emirates hire year round or is it just open for a specific amount of time? I saw it said they received 15,000 applications per month so that made me think they accept applications each month of the year.

That was when they were in a huge recruiting boom around 2009/2010.

Nowaday they do tend to stop recruitment once they get a lot of applications, so if it is open best to submit an application in case it closes. Sometimes it's only for a month, other times it closes and they won't recruit again for a year.