Closet dome light, is the tinfoil necessary?
That is a reflective sheet to help use more of your bulbs' light output. So if you want the same sort of brightness as you had, yep, you do need to replace it. But for a closet, I personally wouldn't bother.

The maximum wattage should be stamped somewhere on the light. If in doubt, use LEDs or similar bulbs that don't push out as much heat as the equivalent CFL or incandescent.