I can’t say I have an explanation for the greasy/wet fur… Pomandcourt had some good ideas to check out with the water-bottle or change in diet.
If I were to go based solely on those pictures, I would say it’s just a normal molt-pattern; in which case I wouldn’t worry too much and just keep an eye on her. Extra brushing/combing during molts can help remove excessive loose fur and keep it out of her system. If she doesn’t put up with combs/brushes you can try using a wet hand to remove the loose fur.
Is there anything that she may have stepped in that she could have then rubbed on her face, inadvertently? That would be my only other guess.
And when in doubt, call a rabbit savvy vet and describe the issue at hand. Chances are, if it’s something simple they may be able to advise you over the phone, and if it’s an indication of something more severe they may suggest you bring her in for an exam.