I agree with Aluz, your little one's feathers look to be in great condition
It appears that these feathers really are normal from a routine moult. The brownish goo you may see could be some dried blood inside the sheath; after all, when the feather was growing, it had a blood supply from the body that was cut off after it had finished growing.
You're right about the cere either turning blue in males or brown in females! There's just a few exceptions, though--males which are of the albino, lutino, recessive pied, or dark eyed clear mutations keep their pearly pink ceres their whole life. Most baby boy budgies grow out of them, but these mutations cause the normal blue colour to never appear.
Since you say that Trix really does have a pink cere, and I can see is of a recessive pied mutation, I think you may have a little boy there!
If you can post a clear, in-focus photo of the cere, we'll be able to confirm that for you