fireplace is a bit rusty - is it safe to use?
The comment by Tyson could very well in itself be the answer.

We should not say "Yes" or "No" to the question "Is it safe to use?" because we do not know. We are only seeing one photo. There are much more important things to be inspected before using a fireplace. You can hire a service, and in some areas the local fire department will do the inspection. The fee is typically reasonable.

Is this the main source of heat for the apartment? Has the landlord exclusively included *(or exclueded) its use in the lease? Give the landlord a call to inquire if it is available for your use, and inquire when it was (if it was) inspected &amp; cleaned last.