Your female budgie looks fine to me, her cere is currently showing she is now in breeding condition (dark brown in colour and crusty appearance).
It appears the cere is thicker and there is some growth, it's possible she has a vitamin deficiency problem and this should be addressed by a vet.
As to the outline in the eyes, blue series budgies will usually have bright yellowish almost green neon colour on that very same area surrounding the eyes on the skin on the eyelids will also have some of that colour. You can notice this when your budgie closes or blinks her eye and this is very normal and not cause for concern.
Thank you very much! My wife and I were concerned that it could have been mites or something, just based on some personal reading/research. With that said, with a closer look, I myself notice that the left nare is covered with that brown crust. Do you have any recommendations for handling that?
You're most welcome!
Now that you mention it, I do see that one of the nostrils appears to be blocked and it's likely due to the abnormal growth of the cere.
Given the fact her breathing is compromised, the best thing to do is really to seek professional advice from an avian vet. Depending on the situation, the avian vet may be able to reshape that area in order for your budgie to regain the function of her blocked nostril.
aluz has offered you good advice.
I agree that seeing an Avian Vet would be best since one of your budgie's nares is almost blocked.
Avian Vets have special training to determine the cause of symptoms resulting from illness or trauma.
When you rely on unskilled individuals, you delay effective treatment. This can prolong suffering that may be avoidable.
The bird will often require a more intense, prolonged treatment with a poorer chance of full recover than it would have if you
seek prompt professional diagnosis and treatment at the first sign of illness.
Having your new budgie examined by an Avian Vet allows you to develop a good relationship with the vet in case your bird needs care for an injury or illness in the future. Additionally, it is always helpful for the vet to have a baseline for your bird to refer to should it need future treatment.
To familiarize yourself with the forums, please take the time to read through all of the How To Guides, the FAQs and the stickies located at the top of each section of the forum.
You'll find most of your basic questions are answered after you've read through all of them.