The crossbar is only required when the fixture has a different screw spacing than the box.

If the insulation is about 1/16 inch thick it is NOT 90 C.

Just as a matter of note, most areas allow homeowners to work on their own owner-occupied home's wiring with a permit. If you don't own your apartment, you can't work on the wiring in it; and if you own it but aren't living in it, you can't work on it either.

Changing a light fixture isn't that big a deal. But if I were your landlord I'd tell you that you should call me and I'd have a pro take care of it.

As a property owner, that's in my best interest. You should see some of the hack jobs that my tenants have done (without asking first, of course). :(