If you are a foreign citizen, you must fulfil specific conditions in order to be granted equal status with Danish citizens and receive state educational grant (SU).

Here you'll find a couple of links on suggested budgets to give you an idea about living expenses in Denmark, including rent:

http://studyindenmark.dk/live-in-denmark/bank-budget 

https://international.au.dk/life/lifeindenmark/costofliving/