When removing wallpaper, it pulled off some of the drywall paper. Can texture be put over this, or do I have to replace the drywall?

This can be repaired with drywall joint compound. Get joint compound, a 6" finishing knife, a pan. Knife looks like a big putty knife, pan looks like a bread loaf pan. Put thin coat over damage area. Let it dry and sand smooth. Repeat if necessary.