Brand new budgie with oddly shaped feet, discoloration on cere?

by Jennifer
(Connecticut, USA)

Just brought home a new budgie, age approximately 4 months. When I got it home, I noticed her toes/toenails seem oddly curled and the bird does not wrap them around the perch straight under as my previous bird did, but instead rests the front ones on TOP of the perch.

Am wondering if this is because her nails are too long or her feet are too small currently to reach around the perch?

Also the birds cere seems to have some odd blackish marking and texture which I did not notice until I got it home. Is this scaly face or another parasite problem, and if so will a "bird protector" from a pet store and hung on the cage kill the mites or will I need to use something topical?

The bird is too young to be showing obvious signs of gender right? *Note, picture looks bluish on nose, but it is not, it is more of black/grey in color