Your beautiful little girl is definitely in breeding condition.
Her beak looks like it may have been injured down at the tip - in the second picture it looks as if it is actually cracked (although that may just be an illusion so you will have to be the judge).
If it is cracked, I'd take her to an Avian Vet to have it trimmed or filed so she doesn't catch it on something and split it. Beaks are made of keratin like your fingernails and can split if there is a severe crack in them.
What diet are you feeding your budgie? Her diet will reflect in her overall health including her beak and feathers.
You can take a drop of olive oil and massage it onto her beak (be careful not to get any into her nares) to help with the dryness.
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 about budgies and caring for them will have been answered after you've read through all of them.
Please take the time to read the information in the links I provided.
There is a lot you can learn to help you provide the best possible care for the health and well-being of your darling little girl. :wave: